Inclusion Criteria:

          -  Ability to understand and the willingness to sign a written informed consent document.
             Subject is willing and able to comply with the protocol for the duration of the study
             including undergoing treatment and scheduled visits and examinations including follow
             up.

          -  Participants must have histologically or cytologically confirmed endometrial, ovarian
             (including ovarian epithelial, fallopian tube, primary peritoneal), cervical, vaginal,
             or vulvar cancer that is metastatic or unresectable and for which standard curative or
             palliative measures do not exist or are no longer effective.

          -  Participants must have measurable disease, defined as at least 1 lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded for
             non-nodal lesions and short axis for nodal lesions) as ≥20 mm with conventional
             techniques or as ≥20 mm with spiral CT scan, MRI, or calipers by clinical exam. See
             Section 11 for the evaluation of measurable disease. See also 3.1.10 as all
             measurable/target lesions must not be located within the planned radiation field for
             the expansion cohort.

          -  Patients must have progressive disease following prior therapy. Specifically, patients
             must have progressed on platinum-based chemotherapy.

          -  At least 21 days must have elapsed from prior therapy (chemotherapy or radiation).

          -  Age of 18 years or older. Because no dosing or adverse event data are currently
             available on the use of durvalumab in combination with tremelimumab and radiation in
             patients <18 years of age, children are excluded from this study.

          -  ECOG performance status ≤1 (Karnofsky ≥60%, see Appendix A).

          -  Body weight of greater than 30 kg.

          -  Participants must have normal organ and marrow function as defined below:

               -  Hgb >=9g/dl

               -  Absolute neutrophil count ≥1,500/mcL

               -  Platelets ≥100,000/mcL

               -  Total bilirubin <=1.5 x normal institutional limits.

                  --- This last criterion will not apply to patients with confirmed Gilbert's
                  syndrome (persistent or recurrent hyperbilirubinemia [predominantly unconjugated
                  bilirubin] in the absence of evidence of hemolysis or hepatic pathology), who
                  will be allowed in consultation with their physician.

               -  AST(SGOT)/ALT(SGPT) ≤3 × institutional upper limit of normal

               -  Creatinine within normal institutional limits

                  --- OR

               -  Creatinine clearance >40 mL/min by the Cockcroft-Gault formula (Cockcroft and
                  Gault 1976) or by 24-hour urine collection for determination of creatinine
                  clearance:

               -  Males:

                    -  Creatinine CL (mL/min) = Weight (kg) x (140 - Age)

                    -  72 x serum creatinine (mg/dL)

               -  Females:

                    -  Creatinine CL (mL/min) = Weight (kg) x (140 - Age) x 0.85

                    -  72 x serum creatinine (mg/dL)

          -  Patients must have at least one lesion not previously irradiated (and not within a
             previously irradiated field) for which palliative radiation to the abdomen and/or
             pelvis is potentially indicated and could be safely delivered at the radiation doses
             specified in this protocol. This lesion must not be within the CNS (brain or spinal
             cord), bone or liver, and must not require urgent or emergent palliative radiation
             given the timing of radiation specified on this protocol. Furthermore, this lesion
             must be located in the abdomen or pelvis and measure at least 2 cm (minimum dimension)
             and no greater than 6 cm (maximum dimension). Palliative radiotherapy would entail
             involved-field radiotherapy to a single lesion or region to encompass gross disease;
             whole-abdomen radiotherapy would not be permitted. Patients who received prior vaginal
             brachytherapy would be permitted to receive palliative pelvic radiation. In the
             expansion cohort at the MTD, this lesion must not be the only measurable lesion (as
             defined in 3.1.3) so that it is possible to determine the response rate outside of the
             radiation treatment field.

          -  The effects of durvalumab and tremelimumab on the developing human fetus are unknown.
             For this reason and because radiation is known to be teratogenic, evidence of
             post-menopausal status or negative urinary or serum pregnancy test for pre-menopausal
             patients is required. Women will be considered post-menopausal if they have been
             amenorrheic for 12 months without an alternative medical cause. The following
             age-specific requirements apply:

               -  Women <50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments and if they have luteinizing hormone and follicle stimulating hormone
                  levels in the post-menopausal range for the institution or underwent surgical
                  sterilization (bilateral oophorectomy or hysterectomy).

               -  Women ≥50 years of age would be considered post-menopausal if they have been
                  amenorrheic for 12 months or more following cessation of all exogenous hormonal
                  treatments, had radiation-induced oophorectomy with last menses >1 year ago, had
                  chemotherapy-induced menopause with >1-year interval since last menses, or
                  underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy
                  or hysterectomy).

               -  Women of child-bearing potential who are sexually active with a non-sterilized
                  male partner must agree to use at least 1 method of highly effective
                  contraception (hormonal or barrier method of birth control; abstinence) prior to
                  study entry and for the duration of study participation and for 180 days after
                  the last dose of therapy. Highly effective methods of contraception, defined as
                  those that result in a low failure rate (i.e., less than 1% per year) when used
                  consistently and correctly, are described in section 5.5. Should a woman become
                  pregnant or suspect she is pregnant while she is participating in this study, she
                  should inform her treating physician immediately.

        Exclusion Criteria

          -  Prior exposure to immune-mediated therapy, including anti-PD-1, anti-PD-L1 (including
             durvalumab) or anti-CTLA-4 directed therapy (including tremelimumab). Therapeutic
             anticancer vaccines are not included in this category. Exposure to other
             investigational agents may be permitted after discussion with the Study PI.

          -  Chemotherapy, targeted therapy, biologic or hormonal agents within 3 weeks prior to
             entering the study.

          -  Radiation therapy within 3 weeks prior to entering the study.

          -  Current receipt of any other investigational agents.

          -  Any unresolved toxicity of NCI CTCAE Grade ≥2, including electrolyte abnormalities,
             from previous anticancer therapy, with the exception of alopecia, vitiligo, and the
             laboratory values defined in the inclusion criteria.

               -  Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after
                  consultation with the Study Physician.

               -  Patients with irreversible toxicity not reasonably expected to be exacerbated by
                  treatment with durvalumab or tremelimumab may be included only after consultation
                  with the Study Physician.

          -  Patients with untreated brain metastases, spinal cord compression, or leptomeningeal
             carcinomatosis are excluded from this clinical trial because of their poor prognosis,
             because of symptoms that may arise from inflammatory reactions, and because they often
             develop progressive neurologic dysfunction that would confound the evaluation of
             neurologic and other adverse events. Patients with brain metastases or spinal cord
             compression previously treated with radiation and/or surgery are allowed if local
             treatment was >30 days ago, most recent MRI demonstrates stability or decrease in size
             of all lesions, and the patient has no current neurologic symptoms related to the
             metastases and treatment and no requirement for corticosteroids related to the prior
             treatment.

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to tremelimumab and durvalumab or previous toxicity attributed to
             durvalumab or other PD-1 or PD-L1 directed therapy that led to drug discontinuation.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, uncontrolled hypertension, interstitial lung disease, pneumonitis, active
             peptic ulcer disease or gastritis, active bleeding diatheses, or serious chronic
             gastrointestinal conditions associated with diarrhea.

          -  Pregnant women are excluded from this study because durvalumab and tremelimumab are
             immune checkpoint inhibitors with the potential for teratogenic or abortifacient
             effects, as is radiation therapy.

          -  A nursing mother unwilling to discontinue breastfeeding. Because there is an unknown
             but potential risk for adverse events in nursing infants secondary to treatment of the
             mother with durvalumab, tremelimumab and radiation, breastfeeding should be
             discontinued if the mother is treated with durvalumab, tremelimumab and radiation.

          -  Female patients who are pregnant or breastfeeding or female patients of reproductive
             potential who are not willing to employ effective birth control from screening to 180
             days after the last dose of durvalumab + tremelimumab combination therapy or 90 days
             after the last dose of durvalumab monotherapy, whichever is the longer time period

          -  HIV-positive patients are ineligible due to the risks associated with immune
             checkpoint blockade.

          -  Current or prior use of immunosuppressive medication within 14 days before the first
             dose of durvalumab and tremelimumab. The following are exceptions to this criterion:

               -  Intranasal, inhaled, topical steroids, or local steroid injections (e.g.,
                  intra-articular injection)

               -  Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of
                  prednisone or its equivalent

               -  Steroids as pre-medication for hypersensitivity reactions (e.g., CT scan
                  pre-medication)

          -  Major surgical procedure (as defined by the Investigator) within 28 days prior to the
             first dose of immunotherapy. Note: Local surgery of isolated lesions for palliative
             intent is acceptable.

          -  History of allogeneic organ transplantation

          -  Active or prior documented autoimmune or inflammatory disorders. Patients without
             active disease in the last 5 years may be included after consultation with the study
             physician. This includes: inflammatory bowel disease, such as Crohn's disease or
             ulcerative colitis, and diverticulitis with the exception of diverticulosis;
             sarcoidosis syndrome, or other serious GI chronic conditions associated with diarrhea;
             systemic lupus erythematosus; Wegener syndrome (granulomatosis with polyangiitis);
             myasthenia gravis; Graves' disease; rheumatoid arthritis; hypophysitis; or uveitis.
             The following are exceptions to this criterion:

               -  Vitiligo or alopecia

               -  Hypothyroidism (e,g,, following Hashimoto syndrome) stable on hormone replacement
                  or psoriasis not requiring systemic treatment

               -  Any chronic skin condition that does not require systemic therapy

               -  Celiac disease controlled by diet alone

          -  History of another primary malignancy except for:

               -  Malignancy treated with curative intent and with no known active disease ≥5 years
                  before the first dose of study drug and of low potential risk for recurrence

               -  Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease

               -  Adequately treated carcinoma in situ without evidence of disease (e.g., cervical
                  cancer in situ)

          -  Mean QT interval corrected for heart rate (QTc) ≥470 ms calculated from 3 consecutive
             electrocardiograms (EKGs) using Fridericia's Correction at baseline or before dosing.
             Thereafter, only 1 EKG is required during visits unless an abnormality is found and in
             which case, confirmation by triplicate EKGs will be needed.

          -  History of active primary immunodeficiency

          -  Known history of previous clinical diagnosis of tuberculosis

          -  Active infection including hepatitis B (known positive HBV surface antigen [HBsAg]
             result) or hepatitis C. Patients with a past or resolved HBV infection (defined as the
             presence of hepatitis B core antibody [anti-HBc] and absence of HBsAg) are eligible.
             Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain
             reaction is negative for HCV RNA.

          -  Receipt of live attenuated vaccine within 30 days prior to the first dose of
             investigational treatment. Note: patients, if enrolled, should not receive live
             vaccine during the study and up to 30 days after the last dose of investigational
             treatment.

          -  Psychiatric illness/social situations that would limit compliance with study
             requirements or compromise the ability of the subject to give written informed consent

          -  Any condition that, in the opinion of the Investigator, would interfere with
             evaluation of the investigational treatment or interpretation of patient safety or
             study results.