I. Assess the toxicities of the combination of cediranib and olaparib in the treatment of recurrent ovarian, fallopian tube, or peritoneal cancer or metastatic triple-negative breast cancer. (Phase I) II. Assess clinical benefit, progression-free survival, and overall survival for patients treated with cediranib and olaparib. (Phase I) III. Assess tumor response, clinical response benefit (response or stable disease as defined by Response Evaluation Criteria in Solid Tumors [RECIST] response criteria x 16 weeks), and overall survival (OS) for patients treated with cediranib and olaparib at the recommended phase II dose (RP2D) as compared with patients receiving olaparib alone. (Phase II) IV. Assess the toxicities of the combination of cediranib and olaparib (tablet formulation) in the treatment of recurrent ovarian, fallopian tube, or peritoneal cancer. (Phase I-T) V. Assess clinical benefit, progression-free survival, and overall survival for patients treated with cediranib and olaparib (tablet formulation). (Phase I-T) VI. Assess the pharmacokinetic profile of cediranib and olaparib (tablet formulation) when administered in combination. (Phase I-T)