Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed ovarian cancer,
             peritoneal cancer or fallopian tube cancer and must have a histological diagnosis of
             either serous or endometrioid cancer based on local histopathological findings; both
             endometrioid and serous histology should be high-grade for eligibility of non-mutation
             carriers; patients with clear cell, mixed epithelial, undifferentiated carcinoma, or
             transitional cell carcinoma histologies are also eligible, provided that the patient
             has a known deleterious germline BRCA1 or BRCA2 mutation identified through testing at
             a clinical laboratory

               -  Note: Due to the long acceptance of BRCA testing through Myriad, Myriad testing
                  will be accepted; if testing for BRCA is done by other organizations,
                  documentation from a qualified medical professional (e.g., ovarian cancer
                  specialty physician involved in the field, high risk genetics physician, genetics
                  counselor) listing the mutation and confirming that the laboratory results showed
                  a recognized germ line deleterious BRCA 1 or BRCA 2 mutation or BRCA
                  rearrangement is required; a copy of Myriad or other BRCA mutational analysis
                  (positive or variants of unknown significance [VUS] or negative) reports will be
                  requested but not required for study enrollment

          -  Patients should have recurrent platinum-resistant or- refractory disease - defined as
             disease that has progressed by imaging while receiving platinum or had recurrence
             within 6 months of the last receipt of platinum-based chemotherapy; rising CA125 only
             is not considered as platinum-resistant or refractory disease

          -  Phase II study: measurable disease by RECIST 1.1 criteria; if archival tumor sample is
             not available tumor sample from fresh biopsy is acceptable

          -  Phase III study: evaluable disease - defined as RECIST 1.1 measurable disease OR
             non-measurable disease (defined as solid and/or cystic abnormalities on radiographic
             imaging that do not meet RECIST 1.1 definitions for target lesions OR ascites and/or
             pleural effusion that has been pathologically demonstrated to be disease-related in
             the setting of a cancer antigen [CA]125 >= 2 x upper limit of normal [ULN])

          -  No more than 3 prior treatment regimens (including primary therapy; no more than 1
             prior non-platinum based therapy in the platinum-resistant/-refractory setting);
             hormonal therapies used as single agents (i.e. tamoxifen, aromatase inhibitors) will
             not count towards this line limit

          -  Patients may not have had a prior anti-angiogenic agent in the recurrent setting;
             prior use of bevacizumab in the upfront or upfront maintenance setting is allowed

          -  Patients may not have previously received a PARP-inhibitor

          -  Patient must have provided study specific informed consent prior to study entry

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 or 2

          -  Absolute neutrophil count >= 1,500/mcL

          -  Platelets >= 100,000/mcL

          -  Hemoglobin >= 10 g/dL

          -  Total bilirubin within =< 1.5 times the upper limit of normal (ULN) institutional
             limits

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 3 x institutional ULN; if intrahepatic liver metastases are present, AST and ALT
             must be =< 5 times institutional ULN

          -  Creatinine =< 1.5 x the institutional ULN

          -  Urine protein: creatinine ratio urine protein creatinine (UPC) of =< 1 OR less than or
             equal to 2+ proteinuria on two consecutive dipsticks taken no less than 1 week apart;
             UPC is the preferred test; patients with 2+ proteinuria on dipstick must also have a
             24-hour urine collection demonstrating protein of =< 500 mg over 24 hours

          -  Toxicities of prior therapy (excepting alopecia) should be resolved to less than or
             equal to grade 1 as per CTCAE; patients with long-standing stable grade 2 neuropathy
             may be considered after discussion with the study chair.

          -  Adequately controlled blood pressure (systolic blood pressure [SBP] =< 140; diastolic
             blood pressure [DBP] =< 90 mmHg) on maximum of three antihypertensive medications;
             patients must have a BP of =< 140/90 mmHg taken in the clinic setting by a medical
             professional within 2 weeks prior to starting study; it is strongly recommended that
             patients who are on three antihypertensive medications be followed by a cardiologist
             or a primary care physician for management of BP while on protocol; patients must be
             willing and able to check and record daily blood pressure readings; blood pressure
             cuffs will be provided to patients randomized to cediranib alone and the combination
             of olaparib and cediranib arms

          -  Adequately controlled thyroid function, with no symptoms of thyroid dysfunction and
             thyroid-stimulating hormone (TSH) within normal limits

          -  Able to swallow and retain oral medications and without gastrointestinal (GI)
             illnesses that would preclude absorption of cediranib or olaparib

          -  Cediranib has been shown to terminate fetal development in the rat, as expected for a
             process dependent on VEGF signaling; for this reason, women of child-bearing potential
             must have a negative pregnancy test prior to study entry; women of child-bearing
             potential must agree to use two reliable forms of contraception (hormonal or barrier
             method of birth control; abstinence) prior to study entry, for the duration of study
             participation, and for 6 weeks after cediranib discontinuation; should a woman become
             pregnant or suspect she is pregnant while participating in this study, she should
             inform her treating physician immediately

          -  Olaparib adversely affects embryofetal survival and development in the rat; for this
             reason, women of child-bearing potential must have a negative pregnancy test prior to
             study entry; women of child-bearing potential must agree to use must agree to use two
             reliable forms of contraception (hormonal or barrier method of birth control;
             abstinence) prior to study entry, for the duration of study participation, and for 3
             months after the last dose of olaparib; should a woman become pregnant or suspect she
             is pregnant while participating in this study, she should inform her treating
             physician immediately

        Exclusion Criteria:

          -  Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for
             nitrosoureas or mitomycin C) of starting treatment or those who have not recovered
             from adverse events due to agents administered more than 4 weeks earlier; patients may
             not have had hormonal therapy within 2 weeks prior to entering the study; patients
             receiving raloxifene for bone health as per Food and Drug Administration (FDA)
             indication may remain on raloxifene absent other drug interactions

          -  Any other investigational agents within the past 4 weeks

          -  Prior treatment affecting the VEGF/VEGFR pathway or the angiopoietin pathway in the
             recurrent setting, including but not limited to thalidomide, bevacizumab, sunitinib,
             sorafenib, pazopanib, cediranib, nintedanib, and trebananib; bevacizumab used in the
             upfront setting in conjunction with chemotherapy and/or as maintenance to treat newly
             diagnosed disease will be allowed

          -  Prior use of PARP-inhibitors

          -  CA-125 only disease without Response Evaluation Criteria in Solid Tumors (RECIST) 1.1
             measurable or otherwise evaluable disease

          -  Major surgical procedure, open biopsy, or significant traumatic injury within 28 days
             prior to starting cediranib

          -  Current signs and/or symptoms of bowel obstruction or signs and/or symptoms of bowel
             obstruction within 3 months prior to starting study drugs

          -  History of intra-abdominal abscess within the past 3 months

          -  History of gastrointestinal perforation; patients with a history of abdominal fistula
             will be considered eligible if the fistula was surgically repaired or has healed,
             there has been no evidence of fistula for at least 6 months, and patient is deemed to
             be at low risk of recurrent fistula

          -  Dependency on IV hydration or total parenteral nutrition (TPN)

          -  Any concomitant or prior invasive malignancies with the following curatively treated
             exceptions:

               -  Treated limited stage basal cell or squamous cell carcinoma of the skin

               -  Carcinoma in situ of the breast or cervix

               -  Primary endometrial cancer meeting the following conditions: stage not greater
                  than IA, grade 1 or 2, no more than superficial myometrial invasion, without
                  vascular or lymphatic invasion; no poorly differentiated subtypes, including
                  papillary serous/serous, clear cell, or other Federation of Gynecology and
                  Obstetrics (FIGO) grade 3 lesions

               -  Prior cancer treated with a curative intent with no evidence of recurrent disease
                  5 years following diagnosis and judged by the investigator to be at low risk of
                  recurrence

          -  Patients with untreated brain metastases, spinal cord compression, or evidence of
             symptomatic brain metastases or leptomeningeal disease as noted on computed tomography
             (CT) or magnetic resonance imaging (MRI) scans should not be included on this study,
             since neurologic dysfunction may confound the evaluation of neurologic and other
             adverse events; patients with treated brain metastases and resolution of any
             associated symptoms must demonstrate stable post-therapeutic imaging for at least 6
             months following therapy prior to starting study drug

          -  Patients with any of the following:

               -  History of myocardial infarction within six months

               -  Unstable angina

               -  Resting electrocardiogram (ECG) with clinically significant abnormal findings

               -  New York Heart Association functional classification of III or IV

          -  If cardiac function assessment is clinically indicated or performed: left ventricular
             ejection fraction (LVEF) less than normal per institutional guidelines, or < 55%, if
             threshold for normal not otherwise specified by institutional guidelines

               -  Patients with the following risk factors should have a baseline cardiac function
                  assessment:

                    -  Prior treatment with anthracyclines

                    -  Prior treatment with trastuzumab

                    -  Prior central thoracic radiation therapy (RT), including RT to the heart

                    -  History of myocardial infarction within 6 to 12 months (Patients with
                       history of myocardial infarction within 6 months are excluded from the
                       study)

                    -  Prior history of impaired cardiac function

          -  History of stroke or transient ischemic attack within six months

          -  Clinical significant peripheral vascular disease or vascular disease (aortic aneurysm
             or aortic dissection)

          -  Evidence of coagulopathy or bleeding diathesis; therapeutic anticoagulation for prior
             thromboembolic events is permitted

          -  Evidence suggestive of myelodysplastic syndrome (MDS) or acute myelogenous leukemia
             (AML) on peripheral blood smear or bone marrow biopsy, if clinically indicated

               -  No prior allogeneic bone marrow transplant or double umbilical cord blood
                  transplantation (dUBCT)

          -  Patients may not use any complementary or alternative medicines including natural
             herbal products or folk remedies as they may interfere with the effectiveness of the
             study treatments

          -  Uncontrolled intercurrent illness including, but not limited to ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia (other than atrial fibrillation with controlled ventricular rate), or
             psychiatric illness/social situations that would limit compliance with study
             requirements

          -  Known human immunodeficiency virus (HIV)-positive individuals are ineligible because
             of the potential for pharmacokinetic interactions with cediranib or olaparib; in
             addition, these individuals are at increased risk of lethal infections when treated
             with marrow-suppressive therapy

          -  Participants receiving any medications or substances that are strong inhibitors or
             inducers of CYP3A4 are ineligible

               -  Strong inhibitors and inducers of UGT/PgP should be used with caution

          -  Pregnant women are excluded from this study because cediranib and olaparib are agents
             with the potential for teratogenic or abortifacient effects; because there is an
             unknown but potential risk of adverse events in nursing infants secondary to treatment
             of the mother with cediranib and olaparib, breastfeeding should be discontinued if the
             mother is treated with cediranib or olaparib; these potential risks may also apply to
             other agents used in this study