Inclusion Criteria:

• Participants must have histologically or cytologically confirmed ovarian cancer, peritoneal cancer or fallopian tube cancer and must have a histological diagnosis of either high grade serous or high grade endometrioid cancer based on local histopathological findings; participants with a deleterious BRCA-mutation on a commercial Clinical Laboratory Improvement Amendments (CLIA) assay with other high-grade histologies are also eligible
  • Due to the long acceptance of BRCA testing through Myriad, Myriad testing will be accepted as documentation of a deleterious mutation; 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 show a recognized germline deleterious BRCA1 or BRCA2 mutation or BRCA rearrangements is required to document the presence of a deleterious mutation
• Participants must have measurable disease via Response Evaluation Criteria in Solid Tumors (RECIST) 1.1, defined as at least one 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 >= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam
• Patients may not have received prior poly ADP ribose polymerase (PARP) inhibitors
• Patients may have received but may not have progressed on prior anti-angiogenic therapy in the upfront setting
• For platinum sensitive cohort
  • Cancer that has not progressed within 6 months of the last receipt of platinum-based chemotherapy
  • No limit on the number of platinum-based lines
  • No more than one prior non-platinum based line of therapy in the recurrent setting
• For platinum-resistant or -refractory cohort
  • Disease that has progressed within 6 months of the last receipt of platinum-based chemotherapy
  • No more than 1 prior line of therapy in the platinum-resistant/-refractory setting
  • No limit on number of prior lines received in the platinum-sensitive setting prior to development of platinum-resistance (defined as disease progression within 6 months of platinum-based chemotherapy)
• Hormonal therapies used as single agents (i.e. tamoxifen, aromatase inhibitors) will not count towards line limit considerations
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• Leukocytes >= 3,000/mcL
• Absolute neutrophil count >= 1,500/mcL
• Hemoglobin >= 10 g/dL
• Platelets >= 100,000/mcL
• Total bilirubin =< 1.5 x the institutional upper limit of normal (ULN)
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3 x institutional upper limit of normal
• Creatinine less than or equal to the institutional upper limit of normal or creatinine clearance >= 60 mL/min/1.73 m^2 for participants with creatinine levels above institutional normal
• Proteinuria less than or equal to 1+ proteinuria on two consecutive dipsticks taken no less than week apart, or a urine protein:creatinine (UPC) ration of =< 1
• Coagulation parameters (international normalized ratio [INR], activated partial thromboplastin time [aPTT]) =< 1.25 x ULN institutional limits, except where a lupus anti-coagulant has been confirmed
• Presence of biopsiable disease and willingness to undergo pre-treatment biopsy
• Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and up to 3 months after end of treatment; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately
• Adequately controlled thyroid function, with no symptoms of thyroid dysfunction and thyroid stimulating hormone (TSH) within normal limits
• Patients must be able to tolerate oral medications and not have gastrointestinal illnesses that would preclude absorption of cediranib or olaparib
• Ability to understand and the willingness to sign a written informed consent document
• Willingness to release and confirmed availability of archival tissue sample for research purposes
• Willingness and ability to check and record daily blood pressure readings; blood pressure cuffs will be provided to patients

Exclusion Criteria:

• Participants may not have had chemotherapy or radiation therapy (RT) within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study and must have recovered from adverse events due to agents administered more than 3 weeks earlier; patients should not have received hormonal therapy for treatment of their cancer within 2 weeks of study entry
• Participants should not have received any other investigational agents nor have participated in an investigational trial within the past 4 weeks
• Participants may not have had prior use of poly ADP ribose polymerase (PARP) inhibitors; patients may not have received prior treatment affecting the vascular endothelial growth factor (VEGF) pathway in the recurrent setting, including but not limited to thalidomide, bevacizumab, sunitinib, or sorafenib
• Participants may not have any evidence of ongoing inadequately controlled hypertension (defined as a systolic blood pressure [BP] of > 140 mmHg or a diastolic BP of > 90 mmHg); patients with hypertension may not be on more than three antihypertensive medications for management of their blood pressure (medications that combine two anti-hypertensives into one are considered as two medications); it is strongly recommended that patients who require three antihypertensive medications for baseline management of pre-existing hypertension be actively followed by a cardiologist or blood pressure specialist for management of BP while on protocol
• Participants may not have had any prior history of hypertensive crisis or hypertensive encephalopathy
• Participants may not have had history of abdominal fistula or gastrointestinal perforation; patients with a history of abdominal fistula will be considered eligible if the fistula has healed or was surgically repaired, there has been no evidence of fistula for at least 6 months, and patient is deemed to be at low risk of recurrent fistula
• Participants may not have had a history of intra-abdominal abscess within the past 3 months
• Participants may not have current signs and/or symptoms of bowel obstruction or signs and/or symptoms of bowel obstruction within 3 months prior to starting study drugs
• Participants may not have a dependency on intravenous (IV) hydration or total parenteral nutrition (TPN)
• Participants with any concomitant or prior invasive malignancies are ineligible with the following 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, clear cell, or other International Federation of Gynecology and Obstetrics (FIGO) grade 3 lesions
  • Prior cancer treated with curative intent with no evidence of recurrent disease 3 years following diagnosis and judged by the investigator to be at low risk of recurrence
• Participants with any of the following:
  • History of myocardial infarction within six months
  • Unstable angina
  • New York Heart Association (NYHA) classification of III or IV
• If cardiac function assessment is clinically indicated or performed: participants will be ineligible if left ventricular ejection fraction (LVEF) is less than normal per institutional guidelines, or < 55%, if the threshold for normal is not otherwise specified by institutional guidelines
• Patients with any of 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
  • A NYHA classification of II controlled with treatment
  • Prior history of impaired cardiac function
• Participants may not have had a history of a stroke or transient ischemic attack within six months
• Participants should not have clinically significant peripheral vascular disease or vascular disease (including aortic aneurysm or aortic dissection)
• Participants may not have a major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to starting cediranib
• Participants should not have any uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• 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 are ineligible; screening imaging to rule out brain metastases is not required for screening, but should be performed prior to study enrollment if clinically indicated; patients with treated brain metastases must demonstrate stable post-therapeutic imaging and resolution of any associated symptoms and must be stably off steroids with no symptoms for at least 6 months following therapy prior to starting study drug
• Participants may not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to cediranib or olaparib
• Participants receiving any medications or substances that are strong inhibitors or inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) or moderate inhibitors of CYP3A4 are ineligible; dihydropyridine calcium-channel blockers are permitted for management of hypertension
• Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with cediranib and olaparib
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible
• Participants should not have evidence of coagulopathy or bleeding diathesis; therapeutic anticoagulation for prior thromboembolic events is permitted
• Current use of a prohibited medication; the following medications or non-drug therapies are prohibited:
  • Other anti-cancer therapy while on study treatment
  • Concurrent treatment with bisphosphonates is permitted; however, treatment must be initiated prior to the first dose of study therapy; prophylactic use of bisphosphonates in patients without bone disease is not permitted, except for the treatment of osteoporosis
  • The concurrent use of all herbal supplements is prohibited during the study (including, but not limited to, cannabis, St. John's wort, kava, ephedra [ma huang], ginkgo biloba, dehydroepiandrosterone [DHEA], yohimbe, saw palmetto, or ginseng)
  • Raloxifene is allowed for patients taking it for bone health
• Participants may not have any features suggestive of myelodysplastic syndrome (MDS) or acute myelogenous leukemia (AML) on peripheral blood smear or bone marrow biopsy, if clinically indicated