Inclusion Criteria:

• For the dose escalation cohort, patients must have histologically or cytologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective
• For the dose escalation cohort, patients may have received any number of prior therapies
• For the dose expansion cohort, participants must have histologically or cytologically confirmed diagnosis of either:
  • Ovarian, fallopian tube, or primary peritoneal cancer of high grade serous histology which has recurred despite standard therapy; up to 3 prior lines in the platinum resistant setting (i.e. up to 3 lines after patients have become platinum resistant); patients may have received unlimited lines while platinum sensitive
  • Triple-negative breast cancer (TNBC) which has recurred despite standard therapy; recurrent TNBC needs to have metastatic disease and patients with an in breast recurrence are not eligible; up to 4 prior lines in the recurrent setting for patients with triple-negative breast cancer are allowed
• For the dose expansion cohort, patients with ovarian, fallopian tube or primary peritoneal cancer must have platinum resistant disease defined as progression within 6 months after last platinum regimen; platinum refractory disease is allowed
• For the dose expansion cohort, patients with triple-negative breast cancer may not be BRCA1/2 germline mutation carriers
• There must be availability of a formalin-fixed, paraffin-embedded tumor specimen
• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 (Karnofsky > 60%)
• Life expectancy of greater than 12 weeks
• Leukocytes >= 3,000/mcL
• Hemoglobin >= 10 g/dL with no blood transfusion in the past 28 days
• Absolute neutrophil count >= 1,500/mcL
• Platelets >= 100,000/mcL
• Total bilirubin within normal institutional limits
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 3 x institutional upper limit of normal
• Creatinine =< the institutional upper limit of normal OR creatinine clearance >= 60 mL/min/1.73 m^2 for patients with creatinine levels above institutional normal
• Corrected QT (QTc) =< 450 ms
• Any clinically significant electrolyte imbalance, particularly hypokalemia and hypomagnesemia, should be corrected before treatment
• Pre-study evaluation must include an ophthalmologic exam by an ophthalmologist (not optometrist) and should minimally include visual acuity testing, slit lamp examination, and funduscopic examination; follow up eye-exams will only be performed if subjects develop/report any visual impairment; visual impairment may include peripheral flashes (photopsia), blurred or double vision, floaters, color distortion and dimness, difficulties with light/dark accommodation, tunnel vision or other field defects, halos, apparent movement of stationary objects, and complex disturbances; follow up eye-exams will minimally include visual acuity testing, slit lamp examination, and funduscopic examination; additional testing will be based on symptoms, what is observed and ophthalmologist recommendations
• For the expansion cohort only: measurable disease by RECIST v1.1 with at least one measurable target lesion
• 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 for 3 months after the last dose of study drugs; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of olaparib and/or AT13387 administration
• Patients must be able to swallow tablets and have no significant impairment in gastrointestinal absorption
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier
• All acute, clinically significant treatment-related toxicity from prior therapy, except for alopecia, must have resolved to grade =< 1
• Patients who are receiving any other investigational agents
• Patients with known active or history of brain metastases should be excluded from this clinical trial
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to olaparib and AT13387 used in study
• 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
• Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with olaparib or AT13387
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible
• Known history of QT/QTc prolongation or torsades de pointes (TdP); patients who are currently receiving treatment with medication with a known risk to prolong the QT interval or inducing torsades de pointes and the treatment cannot either be discontinued or switched to a different medication prior to starting study drugs
• Participants receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 or moderate inhibitors of CYP3A4 are ineligible; the study team should check a frequently-updated medical reference for a list of drugs to avoid or minimize use of; as part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
• Participants with myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML)