Inclusion Criteria:

          -  Patients must have platinum-sensitive or platinum-resistant recurrent or persistent or
             refractory ovarian, fallopian tube, or primary peritoneal carcinoma AND have one or
             more of the following characteristics documented on a validated platform (documented
             genetic test report is required). Historic report is permitted.

          -  A germline BRCA1 or BRCA2 deleterious alteration.

          -  A somatic mutation in BRCA1 or BRCA2 detected in a tumor sample or on circulating
             tumor DNA

          -  Carry a known or likely loss of function alteration in one or more of the homologous
             recombination or mismatch repair pathways genes

          -  Demonstrate a genomic phenotype of HR deficiency as measured by a LOH-high score.

               -  Recurrent ovarian cancer is defined as recurrence of disease in a patient who
                  achieved initial complete response to primary therapy

               -  Persistent ovarian cancer is defined as having residual disease in the form of
                  elevated tumor markers or microscopic or clinically evident disease in a patient
                  who has completed and apparently responded to initial chemotherapy

               -  Refractory ovarian cancer is defined as patients who have failed to achieve at
                  least a partial response to therapy including patients with either stable disease
                  or disease progression during primary therapy

               -  Platinum-sensitive is defined as achievement of documented response to initial
                  platinum-based treatment and has been off treatment for an extended period of
                  time (more than 6 months)

               -  Platinum-resistant is defined as relapse within 6 months of last platinum-based
                  chemotherapy or progression while on platinum-based therapy

          -  All patients must have measurable disease as defined by immune-related Response
             Evaluation Criteria in Solid Tumors (irRECIST); measurable disease is defined as 10 mm
             in the longest diameter by computed tomography (CT) or magnetic resonance imaging
             (MRI) scan (or no less than double the slice thickness) for non- nodal lesions and >=
             15 mm in short axis for nodal lesions, 20 mm by chest X-ray, a lymph node must be >=
             15 mm in short axis when assessed by CT scan (CT scan slice thickness recommended to
             be no greater than 5 mm)

          -  Must have archival tissue available for PD-L1 assessment

          -  Patients should be free of active infection requiring antibiotics (with the exception
             of uncomplicated urinary tract infection [UTI])

          -  Patients who have the following risk factors are considered to be at increased risk
             for cardiac toxicities and may be enrolled only with increased monitoring: i) prior
             treatment with anthracyclines; ii) prior treatment with trastuzumab; iii) a New York
             Heart Association classification of II controlled with treatment; iv) prior central
             thoracic radiation therapy (RT), including RT to the heart

          -  Any hormonal therapy being taken as a treatment for cancer must be discontinued at
             least one week prior to registration; continuation of hormone replacement therapy e.g.
             thyroid hormone replacement therapy is permitted

          -  Able to tolerate oral medications and no GI illnesses that would preclude absorption
             of olaparib

          -  Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0-1

          -  Life expectancy of > 6 months

          -  Hemoglobin >= 10 g/dL (no blood transfusion in the 28 days prior to entry [olaparib
             guidelines])

          -  White blood cell count (WBC) > 3 x 10^9/L

          -  Absolute neutrophil count (ANC) >= 1.5 x 10^9/L (>=1500 per mm^3)

          -  Platelet count >= 100 x 10^9/L (>= 100,000 per mm^3)

          -  Serum bilirubin =< 1.5 x institutional upper limit of normal (ULN); this will not
             apply to subjects with confirmed Gilbert's syndrome (persistent or recurrent
             hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or
             hepatic pathology), who will be allowed only in consultation with their physician

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional upper limit of normal unless liver metastases are present, in
             which case it must be =< 5 x ULN

          -  Creatinine =< 1.5 x ULN, serum creatinine clearance (CL) > 51 ml/min (by the
             Cockcroft- Gault equation)

          -  Female subjects must either be of non-reproductive potential (i.e., post-menopausal by
             history: >= 60 years old and no menses for >=1 year without an alternative medical
             cause; OR history of hysterectomy, OR history of bilateral tubal ligation, OR history
             of bilateral oophorectomy) or must have a negative serum pregnancy test within 28 days
             of study treatment, confirmed prior to treatment on day 1

          -  Participants of child-bearing potential must agree to use two highly effective and
             acceptable forms of contraception from screening, throughout their participation in
             the study and for 180 days after the last dose of durvalumab + tremelimumab
             combination therapy or 90 days after last dose of durvalumab or olaparib, whichever is
             the longer time period (e.g., hormonal or barrier method of birth control); 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

          -  Participant or legal representative must understand the investigational nature of this
             study and sign an Independent Ethics Committee/Institutional Review Board approved
             written informed consent form prior to receiving any study related procedure

          -  Subject is willing and able to comply with the protocol for the duration of the study
             including undergoing treatment and scheduled visits and examinations including follow
             up

        Exclusion Criteria:

          -  Involvement in the planning and/or conduct of the study (applies to both AstraZeneca
             staff and/or staff at the study site); previous enrollment in the present study

          -  Participation in another clinical study with an investigational product during the
             last 4 weeks (prior use of bevacizumab in the upfront setting is allowed)

          -  History of discontinuation of any previous treatment with PARP inhibitors, including
             olaparib, or a PD-1 or PD-L1 inhibitor, including durvalumab or anti-CTLA4 antibody,
             including tremelimumab due to toxicity.

          -  Patients with myelodysplastic syndrome/acute myeloid leukemia

          -  History and/or confirmed interstitial lung disease (ILD)/pneumonitis, extensive
             bilateral lung disease on high-resolution computed tomography (HRCT) scan

          -  Concomitant use of a strong CYP3A inhibitors (e.g., itraconazole, telithromycin,
             clarithromycin, ketoconazole, voriconazole, nefazodone, posaconazole, ritonavir,
             lopinavir/ritonavir, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) and
             moderate CYP3A inhibitors (e.g., amprenavir, aprepitant, atazanavir, ciprofloxacin,
             crizotinib, darunavir/ritonavir, diltiazem, erythromycin, fluconazole. Fosamprenavir,
             imatinib, verapamil)

          -  Concomitant use of strong CYP3A inducers (e.g., phenytoin, rifampicin, carbamazepine,
             St. John's wort) and moderate CYP3A inducers (e.g., bosentan, efavirenz, etravirine,
             modafinil, nafcillin)

          -  History of another primary malignancy except for:

               -  Malignancy treated with curative intent and with no known active disease >= 5
                  years before the first dose of study drug and of low potential risk for
                  recurrence

               -  Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease (e.g. basal cell or squamous cell carcinoma of the skin)

               -  Adequately treated carcinoma in situ without evidence of disease (e.g., breast
                  and cervical cancer in situ)

          -  Receipt of the last dose of anti-cancer therapy (chemotherapy, immunotherapy,
             endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal
             antibodies, radiotherapy or other investigational agent) =< 21 days prior to the first
             dose of study drug and within 6 weeks for nitrosourea or mitomycin C)

          -  Mean QT interval corrected for heart rate (QTcF) >= 470 ms calculated from 3
             electrocardiograms (ECGs) using Fridericia's correction

          -  Patients with history of myocardial infarction within 6 months

          -  Current or prior use of immunosuppressive medication within 28 days before the first
             dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or
             systemic corticosteroids at physiological doses, which are not to exceed 10 mg/day of
             prednisone, or an equivalent corticosteroid

          -  Any unresolved toxicity (Common Terminology Criteria for Adverse Events [CTCAE] grade
             >= 2) from previous anti-cancer therapy; subjects with irreversible toxicity that is
             not reasonably expected to be exacerbated by the investigational product may be
             included (e.g., hearing loss, peripherally neuropathy)

          -  Any prior grade >= 3 immune-related adverse event (irAE) while receiving any previous
             immunotherapy agent, or any unresolved irAE > grade 1

          -  Active or prior documented autoimmune disease within the past 2 years; NOTE: Subjects
             with vitiligo, Grave's disease, or psoriasis not requiring systemic treatment (within
             the past 2 years) are not excluded

          -  Active or prior documented inflammatory bowel disease (e.g., Crohn?s disease,
             ulcerative colitis)

          -  Patients with thyroid dysfunction if not adequately controlled

          -  History of primary immunodeficiency

          -  History of allogeneic organ transplant

          -  History of hypersensitivity to durvalumab, tremelimumab, olaparib or, any excipient

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable
             angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, active
             bleeding diatheses including any subject known to have evidence of, or test positive
             for, acute or chronic hepatitis B, hepatitis C or human immunodeficiency virus (HIV),
             or psychiatric illness/social situations that would limit compliance with study
             requirements or compromise the ability of the subject to give written informed consent

          -  Known history of previous clinical diagnosis of tuberculosis

          -  History of leptomeningeal carcinomatosis

          -  Receipt of live attenuated vaccination within 30 days prior to study entry or within
             30 days of receiving durvalumab (e.g. live attenuated influenza vaccine [LAIV],
             measles/mumps/rubella vaccine [MMR], variola virus vaccine [VAR], zoster, yellow
             fever, etc.)

          -  Female subjects who are pregnant, breast-feeding, or of reproductive potential who are
             not employing an effective method of birth control from screening to 180 days after
             the last dose of durvalumab + tremelimumab + olaparib combination therapy or 90 days
             after the last dose of durvalumab and olaparib therapy, whichever is the longer time
             period

          -  Any condition that, in the opinion of the investigator, would interfere with
             evaluation of study treatment or interpretation of patient safety or study results or,
             is an unsuitable candidate to receive study drug (e.g. inability to tolerate oral
             medications which would preclude absorption of olaparib)

          -  Symptomatic or uncontrolled brain metastases requiring concurrent treatment, inclusive
             of but not limited to surgery, radiation and/or corticosteroids

          -  Subjects with uncontrolled seizures

          -  Dependency on IV hydration or total parenteral nutrition (TPN)