Olaparib in People With Malignant Mesothelioma

* INCLUSION CRITERIA: * Patients must have histologically or cytologically malignant mesothelioma confirmed by the National Cancer Institute (NCI) Laboratory of Pathology. Patients with pleural, peritoneal, pericardial or tunica vaginalis mesothelioma are eligible. * Archival tumor samples must be available and sufficient for diagnostic and genetic testing; if archival sample insufficient for testing, subject must have lesions amenable to biopsy and be willing to undergo biopsy. * Patients must have measurable disease. * Patients must have progressive disease at study entry * Patients must have received prior platinum and pemetrexed based therapies. Response to platinum is not an eligibility criterion for enrollment. * Age greater than or equal to 18 years. Because no dosing or adverse event data are currently available on the use of olaparib in patients \<18 years of age, children are excluded from this study, but may be eligible for future pediatric trials. * Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 1. * Patients must have a life expectancy of greater than or equal to 16 weeks * Patients must have adequate organ and marrow function less than or equal to 5 days prior to Cycle 1 Day 1 (C1D1) as defined below: * leukocytes greater than or equal to 3,000/mcL * absolute neutrophil count greater than or equal to greater than or equal to 1,500/mcL without growth factor support * platelets greater than or equal to 100,000/mcL * hemoglobin greater than or equal to 10 g/dL with no blood transfusion in the past 28 days * total bilirubin less than or equal to 1.5 x upper limits of normal (ULN) (unless Gilbert's Disease) * Aspartate aminotransferase (AST) Serum glutamic oxaloacetic transaminase (SGOT)/Alanine aminotransferase (ALT) Serum glutamic-pyruvic transaminase (SGPT) less than or equal to 2.5 X institutional upper limit of normal (less than or equal to 5 X ULN in the presence of liver metastases) * creatinine clearance greater than or equal to 51 mL/min (calculated using the -Cockcroft-Gault formula. * Pre-clinical data indicate that olaparib can have adverse effects on embryofetal survival and development. It is further not known whether olaparib or its metabolites are found in seminal fluid. For these reasons: * Women of childbearing potential and their partners, who are sexually active, must agree to the use of 2 highly effective forms of contraception in combination (male condom plus one other method or must totally/truly abstain from any form of sexual intercourse. This should be started from the signing of the informed consent, throughout their participation in the study and for at least 1 month after the last dose of olaparib. * Male patients must use a condom during treatment and for 3 months after the last dose of olaparib when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential. Male patients should not donate sperm throughout the period of taking olaparib and for 3 months following the last dose of olaparib. * Acceptable birth control methods: * Total sexual abstinence i.e., refrain from any form of sexual intercourse in line with the patients usual and/or preferred lifestyle. Abstinence must be for the total duration of the study treatment and for at least 1 month (for female patients) or 3 months (for male patients) after the last dose of study treatment. Periodic abstinence (e.g., calendar ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception. * Vasectomised sexual partner PLUS male condom. With participant assurance that partner received post-vasectomy confirmation of azoospermia. * Tubal occlusion PLUS male condom * Intrauterine Device PLUS male condom. Provided coils are copper-banded. * Etonogestrel implants (e.g., Implanon, Norplant) PLUS male condom * Normal and low dose combined oral pills PLUS male condom * Hormonal shot or injection (e.g., Depo-Provera) PLUS male condom * Intrauterine system device (e.g., levonorgestrel-releasing intrauterine system -Mirena) PLUS male condom * Norelgestromin/ethinyl estradiol transdermal system PLUS male condom * Intravaginal device (e.g., ethinyl estradiol and etonogestrel) PLUS male condom * Cerazette (desogestrel) PLUS male condom. Cerazette is currently the only highly efficacious progesterone based pill. * Ability of subject to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Patients who are receiving any other investigational agents. * Patients who have received any previous treatment with a Poly (ADP-ribose) polymerase (PARP) inhibitor, including olaparib. * Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 3 weeks prior to study treatment * Patients with other malignancy documented as occurring within the last 1 year except: adequately treated nonmelanoma skin cancer, curatively treated in situ cancer of the cervix, ductal carcinoma in situ (DCIS), Stage 1, grade 1 endometrial carcinoma, or other solid tumors including lymphomas (without bone marrow involvement) documented as curatively treated or under control for greater than or equal to 1 year. * Patients with features suggestive of Myelodysplastic syndromes (MDS) and acute myeloid leukemia (AML) on peripheral blood smear. * Patients with symptomatic uncontrolled brain metastases. A scan to confirm the absence of brain metastases is not required. The patient can receive a stable dose of corticosteroids before and during the study as long as these were started at least 4 weeks prior to treatment. Patients with spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days. * History of allergic reactions or hypersensitivity attributed to compounds of similar chemical or biologic composition to olaparib or its excipients. * Patients who have had a whole blood transfusion within 120 days prior to enrollment. (Packed red blood cells and platelet transfusions are acceptable) * Patients with persistent toxicities (greater than or equal to Common Terminology Criteria for Adverse Events (CTCAE) grade 2) with the exception of alopecia,caused by previous cancer therapy * Concomitant use of known strong or moderate cytochrome P450, family 3 (CYP3A) inhibitors (e.g. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting olaparib is 2 weeks. * Concomitant use of known strong CYP3A inducers (e.g. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (e.g. bosentan, efavirenz, modafinil). The required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents. * Resting electrocardiogram (ECG) with Fridericia's formula (QTcF) \> 470 msec on 2 or more time points within a 24-hour period or family history of long Q wave, T wave (QT) syndrome * Patients that have had major surgery within 2 weeks of starting study treatment and patients must have recovered from any effects of any major surgery. * Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication. * Patients considered a poor medical risk due to a serious, uncontrolled medical disorder, non-malignant systemic disease or active, uncontrolled infection. Examples include, but are not limited to, uncontrolled ventricular arrhythmia, recent (within 3 months) myocardial infarction, uncontrolled major seizure disorder, unstable spinal cord compression, superior vena cava syndrome, extensive interstitial bilateral lung disease on High Resolution Computed Tomography (HRCT) scan or any psychiatric disorder that prohibits obtaining informed consent. * Pregnant women are excluded from this study because olaparib has the potential for teratogenic or abortifacient effects. Women must either be post-menopausal or must have a negative pregnancy test (urine or serum) less than or equal to 28 days prior to enrollment and confirmed on day 1 of cycle 1 of study therapy. Postmenopausal is defined as: Amenorrheic for 1 year or more following cessation of exogenous hormonaltreatments Luteinizing hormone (LH) and Follicle stimulating hormone (FSH) levels in the post-menopausal range for women under 50 years of age radiation-induced oophorectomy with last menses \>1 year ago chemotherapy-induced menopause with \>1-year interval since last menses surgical sterilisation (bilateral oophorectomy or hysterectomy) * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with olaparib, breastfeeding should be discontinued if the mother is treated with olaparib. * Immunocompromised patients are excluded. * Patients who are known to be serologically positive for human immunodeficiency virus (HIV). This includes HIV patients on antiretroviral therapy due to the potential for pharmacokinetic interactions with olaparib. * Patients with known active hepatitis (i.e. Hepatitis B or C) due to risk of transmitting the infection through blood or other body fluids * Previous allogeneic hematopoietic stem cell transplant, allogeneic bone marrow transplant or double umbilical cord blood transplant (duCBT)