Testing the Combination of the Study Drugs Cediranib and Olaparib in Recurrent Ovarian Cancer

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 CT scan, MRI, or calipers by clinical exam * Patients may not have received prior poly ADP ribose polymerase (PA…