I. To assess correlation of homologous recombination deficiency (HRD) status, as assessed via BROCA-HR assay with response, as measured by PFS and ORR. (Phase II) II. To evaluate the prognostic and predictive role of circulating endothelial cells (CEC) on comparative effectiveness of targeted therapies and reference chemotherapy. (Phase II) III. To evaluate quality of life data compliance, as measured by the 9-item Disease Related Symptoms (DRS-9) subscale of the National Comprehensive Cancer Network (NCCN)-Functional Assessment of Cancer Therapy (FACT) Ovarian Symptom Index (NFOSI) for utilization and analysis in the Phase III study. (Phase II) IV. To assess exploratory biomarkers of potential HRD, including genomic scarring, BRCA1 methylation, BRCA1 protein expression, and mutations in NHEJ, and other genes that might modify HRD. (Phase II and Phase III) V. To evaluate the prognostic and predictive role of angiogenic biomarkers, as assessed by the Duke plasma angiome. (Phase II and Phase III) VI. To assess correlation of HRD status, as assessed via BROCA-HR assay with response, as measured by OS, PFS and ORR. (Phase III) VII. To evaluate the prognostic and predictive role of circulating endothelial cells (CEC) on comparative effectiveness of targeted therapies and reference chemotherapy. (Phase III) VIII. To assess the effect on disease-related symptoms (DRS) as measured by the 9-item DRS-P subscale of the NCCN-FACT Ovarian Symptom Index-18 (NFOSI-18), of single agent olaparib or cediranib and combination, compared to standard chemotherapy, in the setting of recurrent platinum-resistant or-refractory ovarian, primary peritoneal or fallopian tube cancer. (Phase III) IX. To assess the effect on secondary measures of quality of life, as assessed by the treatment side effects (TSE) and function/well-being (F/WB) subscales of the NFOSI-18, sensory neuropathy as measured by the FACT/GOG-Ntx-4, and health utility as measured by the EQ-5D, of single agent olaparib or cediranib and combination, compared to standard chemotherapy, in the setting of recurrent platinum-resistant or-refractory ovarian, primary peritoneal or fallopian tube cancer. (Phase III)