Inclusion Criteria:

          -  Step 1 (Registration) Inclusion

          -  Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status of
             0-2 at the time of registration

          -  Patient must have histologically proven pure or mixed urothelial cancer of the bladder

               -  NOTE: Small cell carcinoma is excluded, however other variant histologies are
                  permitted provided a component of urothelial carcinoma is present

          -  Prior to receiving any induction chemotherapy, patient must have documented
             node-positive and non-metastatic disease (any T, N1-2 M0). Patients with clinical N3
             disease are ineligible.

               -  NOTE: Node positivity will be defined by the official interpretation of imaging
                  studies. Positive lymph nodes must be imaging read with suspicious lymph node
                  (LN) >= 1.0 cm in short axis to be eligible, with or without biopsy as documented
                  by a radiologist at the treating center. LN Biopsy is not mandatory but
                  encouraged if feasible and safe per physician discretion. Patients with a
                  negative biopsy of nodes determined to be suspicious on imaging are not eligible.
                  Please note that for non-muscle invasive disease on TURBT, node-positive disease
                  MUST be biopsy proven for patient to be eligible

          -  Induction Chemotherapy Requirements

               -  For patients registered to this protocol post-completion of induction systemic
                  chemotherapy:

                    -  Patient must have received at least 3 cycles of induction chemotherapy
                       (cisplatin-based chemotherapy OR non-cisplatin based chemotherapy) with no
                       evidence of progressive disease (PD) on post-chemotherapy imaging. The end
                       of last cycle of induction chemotherapy must be within 12 weeks of
                       registration

                    -  Patient who have received more than 3 cycles of induction systemic
                       chemotherapy are also eligible

                    -  Patient must have had a CR, PR or SD to induction chemotherapy on standard
                       imaging

                         -  NOTE: Patients who have only received 2 cycles of induction
                            chemotherapy and demonstrated clinical response (complete response [CR]
                            OR partial response [PR], OR stable disease [SD]) may be considered for
                            enrollment only after consultation and approval by the study chair
                            under exceptional circumstances where 3rd cycle cannot be delivered.
                            Documentation of correspondences with the study chair must be kept on
                            file. We encourage all patients to get 3 cycles of induction
                            chemotherapy

               -  For patients registered to this protocol prior to starting induction systemic
                  chemotherapy:

                    -  Patient must agree to a planned treatment with 3 cycles of induction
                       chemotherapy (physician's choice)

                    -  Patient will again be restaged after completion of induction chemotherapy
                       and prior to randomization to chemoRT +/- MEDI4736 (durvalumab)

                    -  Patient must have a CR, PR or SD to induction chemotherapy on standard
                       imaging prior to randomization to chemoradiotherapy

          -  Patient must not have presence of concomitant active upper tract tumors or urethra
             tumors. History of previously adequately treated non-muscle invasive bladder cancer
             (NMIBC) are eligible; previously treated urothelial cancer or histological variant at
             any site outside of the urinary bladder are allowed, provided they have been
             Ta/T1/carcinoma in situ (CIS) and post treatment follow up imaging and endoscopic
             evaluation shows no evidence of disease

          -  Patients with previous exposure to immune checkpoint inhibitor for non-muscle invasive
             disease are eligible. If given for NMIBC, the last dose must have been completed > 12
             months prior to registration

          -  For patients registered on the study

               -  Patient must not be pregnant or breast-feeding due to the potential harm to an
                  unborn fetus and possible risk for adverse events in nursing infants with the
                  treatment regimens being used

               -  All patients of childbearing potential must have a blood test or urine study
                  within 14 days prior to registration to rule out pregnancy

               -  A patient of childbearing potential is defined as any patient, regardless of
                  sexual orientation or whether they have undergone tubal ligation, who meets the
                  following criteria: 1) has achieved menarche at some point, 2) has not undergone
                  a hysterectomy or bilateral oophorectomy; or 3) has not been naturally
                  postmenopausal (amenorrhea following cancer therapy does not rule out
                  childbearing potential) for at least 24 consecutive months (i.e., has had menses
                  at any time in the preceding 24 consecutive months)

          -  For patients registered prior to induction chemotherapy only:

               -  Patients of childbearing potential and sexually active patients must not expect
                  to conceive or father children by using accepted and effected method(s) of
                  contraception or by abstaining from sexual intercourse from the time of
                  registration for the duration of their participation in the study and continue
                  for at least 3 months after the last dose of protocol treatment

          -  Leukocytes >= 3,000/mcL (obtained < 14 days prior to registration)

          -  Absolute neutrophil count >= 1,500/mcL (obtained < 14 days prior to registration)

          -  Hemoglobin >= 9 g/dL (obtained < 14 days prior to registration)

          -  Platelets >= 100,000/mcL (obtained < 14 days prior to registration)

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (obtained < 14 days
             prior to registration)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional ULN (obtained < 14 days prior to registration)

          -  Must have adequate renal function as evidenced by calculated (Cockcroft's formula)
             creatinine clearance or 24 hours actual creatinine clearance >= 30mL/min. The
             creatinine used to calculate the clearance result must have been obtained within 14
             days prior to registration. Actual body weight, not ideal body weight, must be used in
             the calculation

          -  Patients with human immunodeficiency virus (HIV) on effective anti-retroviral therapy
             with undetectable viral load within 6 months of registration are eligible for this
             trial

          -  Patients with a prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial. Site is encouraged to discuss
             with the study chair if needed prior to registration

          -  Patients with known history or current symptoms of cardiac disease, or history of
             treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac
             function using the New York Heart Association Functional Classification. To be
             eligible for this trial, patients should be class IIB or better

          -  Step 2 (Randomization) Inclusion Criteria

          -  Patient must have an ECOG performance status of 0-2 at the time of randomization

          -  Patient must undergo selection of concurrent chemotherapy regimen

          -  Patient must agree to undergo CT simulation and treatment planning within two days of
             randomization. If this is the first case registered at the site, then a pre-treatment
             radiation therapy (RT) review will be required and will take up to 3 business days.
             The patient cannot start radiation treatment prior to successful completion of this
             pre-treatment review. Therefore, careful planning is necessary to meet the deadline of
             starting radiation within 15 business days of randomization and within 12 weeks of the
             end of induction chemotherapy

               -  NOTE: Chemoradiotherapy should be planned to start up to 12 weeks after the end
                  of induction chemotherapy, but after imaging and cystoscopic restaging,
                  randomization, and any pretreatment radiation quality assurance (QA) that is
                  required

          -  Patients must not be pregnant or breast-feeding due to the potential harm to an unborn
             fetus and possible risk for adverse events in nursing infants with the treatment
             regimens being used

               -  All patients of childbearing potential must have a blood test or urine study
                  within 14 days prior to registration to rule out pregnancy

               -  A patient of childbearing potential is defined as any patient, regardless of
                  sexual orientation or whether they have undergone tubal ligation, who meets the
                  following criteria: 1) has achieved menarche at some point, 2) has not undergone
                  a hysterectomy or bilateral oophorectomy; or 3) has not been naturally
                  postmenopausal (amenorrhea following cancer therapy does not rule out
                  childbearing potential) for at least 24 consecutive months (i.e., has had menses
                  at any time in the preceding 24 consecutive months)

          -  Patients of childbearing potential and/or sexually active patients must not expect to
             conceive or father children by using accepted and effective method(s) of contraception
             or by abstaining from sexual intercourse at least one week prior to the start of
             treatment and continue for at least 3 months after the last dose of the protocol
             treatment

          -  Leukocytes >= 3,000/mcL (obtained < 14 days prior to randomization)

          -  Absolute neutrophil count >= 1,500/mcL (obtained < 14 days prior to randomization)

          -  Hemoglobin >= 9 g/dL (obtained < 14 days prior to randomization)

          -  Platelets >= 100,000/mcL (obtained < 14 days prior to randomization)

          -  Total bilirubin =< 1.5 x institutional upper limit of normal (ULN) (obtained < 14 days
             prior to randomization)

          -  AST (SGOT)/ALT (SGPT) =< 2.5 x institutional ULN (obtained < 14 days prior to
             randomization)

          -  Must have adequate renal function as evidenced by calculated (Cockcroft's formula)
             creatinine clearance or 24 hours actual creatinine clearance >= 30 mL/min. The
             creatinine used to calculate the clearance result must have been obtained within 14
             days prior to randomization. Actual body weight, not ideal body weight, must be used
             in the calculation

          -  Step 3 (Post chemoRT+/- MEDI4736 [durvalumab], prior to starting adjuvant MEDI4736
             [durvalumab] versus [vs.] observation) Inclusion Criteria

          -  Patient must have evaluation to determine clinical outcome post chemoRT+/- MEDI4736
             (durvalumab) with imaging and cystoscopy with biopsy confirmation to ensure no
             progression and absence of >= T2 disease in the bladder

          -  Patient must have achieved either complete clinical response OR have demonstrated
             clinical benefit prior to continuing onto adjuvant MEDI4736 (durvalumab)

          -  Patients who are to go on the adjuvant MEDI4736 (durvalumab) arm must have recovered
             to at least grade 2 or less immune related adverse events (AE) prior to starting
             treatment except for immune related alopecia, clinically asymptomatic
             endocrinopathies. For patients who may have gotten immune related AEs during chemoRT+
             MEDI4736 (durvalumab), registration could be delayed up to additional 4 weeks to
             ensure recovery to at least grade 2 or lower prior to starting adjuvant therapy.
             However patients with MEDI4736 (durvalumab) related AEs that require permanent
             discontinuation of MEDI4736 (durvalumab) will not continue on the adjuvant treatment
             regardless of the response

          -  ANC >= 1,000 mcL (within 4 weeks of start of day 1 [D1] of adjuvant treatment)

          -  Hemoglobin >= 8 g/dL (within 4 weeks of start of D1 of adjuvant treatment)

          -  Platelets >= 70,000 mcL (within 4 weeks of start of D1 of adjuvant treatment)

          -  Patient on the chemoRT arm must have achieved either complete clinical response OR
             have demonstrated clinical benefit prior to be placed on the observation alone arm

        Exclusion Criteria:

          -  Step 1 (Registration) Exclusion

          -  Patient must not have received any previous radiation therapy to the pelvic area

          -  For patients with autoimmune conditions, patient must not have history of prior
             documented autoimmune disease within the past 2 years

               -  NOTE: Patient with vitiligo, Grave's disease, eczema or psoriasis (not requiring
                  systemic treatment within the past 2 years) are not excluded. Patients with
                  history of completely resolved childhood asthma or atopy are not excluded.
                  Patients with asthma not requiring more than 10 mg/d or equivalent of prednisone
                  are not excluded. Patients with well-controlled hypothyroidism on thyroxine
                  replacement will be eligible as well. Patients with known history of
                  hypoadrenalism on maintenance steroids will be eligible. Patients with type I
                  diabetes mellitus will be eligible, provided their disease is well controlled.
                  History of autoimmune related alopecia is also not an exclusion criteria

               -  Patient with active or prior documented inflammatory bowel disease (e.g., Crohn's
                  disease, ulcerative colitis) are not eligible

               -  Patient with a history of and/or confirmed pneumonitis will not be eligible

               -  Patient with a history of primary immunodeficiency will not be eligible

               -  Patient with history of allogeneic organ transplant are not eligible

          -  Patient must not have clinically significant liver disease that precludes patient from
             treatment regimens prescribed on the study (including, but not limited to, active
             viral, alcoholic or other autoimmune hepatitis, cirrhosis or inherited liver disease)

          -  Patient must not have any unresolved toxicity (National Cancer Institute [NCI] CTCAE
             grade >= 2) from previous anti-cancer therapy with the exception of alopecia,
             vitiligo, and the laboratory values

               -  NOTE: Patients with grade >= 2 neuropathy will be evaluated on a case-by-case
                  basis after consultation with the study chair

               -  NOTE: Patients with irreversible toxicity not reasonably expected to be
                  exacerbated by treatment with MEDI4736 (durvalumab) may be included only after
                  consultation with the study chair. Documentation of correspondences with the
                  study chair must be kept on file

          -  Step 2 (Randomization) Exclusion Criteria

          -  Patient must have no signs of progression (CR/PR or SD) based on restaging imaging and
             cystoscopy after completion of induction chemotherapy, which consists of:

               -  Computed tomography (CT) chest, abdomen, or pelvis. Magnetic resonance imaging
                  (MRI) pelvis can be used instead of CT per treating physician discretion. The
                  imaging must be done within 4 weeks prior to randomization

               -  Cystoscopic evaluation and attempt to perform maximal transurethral resection of
                  bladder tumor (TURBT) performed by the participating urologist ideally within 8
                  weeks but up to 10 weeks is allowed prior to randomization. If maximal TURBT is
                  not possible for medical reasons, the enrollment must be discussed and approved
                  with the study chair. Documentation of correspondences with the study chair must
                  be kept on file

          -  For patients with autoimmune conditions: Patient must not have a history of active or
             prior documented autoimmune disease within the past 2 years

               -  NOTE: Patient with vitiligo, Grave's disease, eczema or psoriasis (not requiring
                  systemic treatment within the past 2 years) are not excluded. Patients with
                  history of completely resolved childhood asthma or atopy are not excluded.
                  Patients with asthma not requiring more than 10mg/d or equivalent of prednisone
                  are not excluded. Patient with well-controlled hypothyroidism on thyroxine
                  replacement will be eligible as well. Patients with known history of
                  hypoadrenalism on maintenance steroids will be e