Inclusion Criteria:

          -  Has read and understands the informed consent form and has given written informed
             consent prior to any study procedures.

          -  Histologically confirmed recurrent epithelial ovarian, primary peritoneal, or
             fallopian tube cancer for which there is no known or established treatment available
             with curative intent.

          -  Have demonstrated progressive disease while taking a PARP inhibitor as a previous
             therapy or within 6 months of completing PARP inhibitor therapy. Response to prior
             PARP inhibitor(i) is not required.

          -  Prior PARP therapy could have been administered as either treatment for recurrent
             disease or as maintenance following prior treatment.

          -  Measurable disease according to RECIST v1.1.

          -  Adequate archived primary or metastatic tumor tissue collected before the prior PARP
             therapy.

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) score of 0-1.

          -  Absolute neutrophil count (ANC) >=1500/L (within 14 days of study drug[s] initiation).

          -  Hemoglobin (Hgb) >= 10 g/dL with no blood transfusion in the past 14 days (within 14
             days of study drug[s] initiation).

          -  Platelets >= 100,000/L (within 14 days of study drug[s] initiation).

          -  Alanine transaminase (ALT) and aspartate transaminase (AST) =< 2.5 x upper limit of
             normal (ULN) or =< 5 x ULN if known hepatic metastases (within 14 days of study
             drug[s] initiation).

          -  Serum bilirubin within normal limits (WNL) or =< 1.5 x ULN in patients with liver
             metastases; or total bilirubin =< 3.0 x ULN with direct bilirubin WNL in patients with
             well documented Gilbert's syndrome (within 14 days of study drug[s] initiation).

          -  Patients should have calculated or measured creatinine clearance of >= 50 mL/min.

          -  Women who are not of child-bearing potential and fertile females of childbearing
             potential who agree to use adequate contraceptive measures, who are not breastfeeding,
             and who have a negative serum pregnancy test within 3 days prior to the start of study
             treatment.

          -  Predicted life expectancy >= 16 weeks.

          -  Willingness and ability to comply with study and follow-up procedures.

        Exclusion Criteria:

          -  Prior Treatment:

               -  PARP inhibitor: Most oral PARP inhibitors (the immediate prior therapy) have a
                  half-life for which 5 half-lives is =< 21 days. Thus, a minimum of 10 days
                  between termination of the prior treatment and administration of olaparib and/or
                  AZD1775 treatment is required. In the event a PARP inhibitor has a longer
                  half-life where 5 half-lives is >= 21 days, treatment of olaparib and/or AZD1775
                  should not begin for 5 half-lives or at least 21 days, whichever is shorter.

               -  Any hormonal therapy directed at the malignant tumor must be discontinued at
                  least one week prior to registration (study enrollment). Continuation of hormone
                  replacement therapy is permitted.

               -  Any other prior therapy directed at the malignant tumor, including immunologic
                  agents, must be discontinued at least three weeks prior to first dose of study
                  drug (6 weeks for nitrosoureas or mitomycin C).

          -  Major surgical procedures =< 28 days of beginning study treatment, or minor surgical
             procedures =< 7 days. No waiting period required following port-a-cath placement.

          -  Grade > 1 toxicity from prior therapy (except alopecia or anorexia).

          -  Patient has an inability to swallow oral medications and patients with
             gastrointestinal disorders likely to interfere with absorption of the study
             medication. Note: Patient may not have a percutaneous endoscopic gastrostomy (PEG)
             tube or be receiving total parenteral nutrition (TPN).

          -  Known central nervous system (CNS) disease other than neurologically stable, treated
             brain metastases - defined as metastasis having no evidence of progression or
             hemorrhage for at least 3 weeks after treatment (including brain radiotherapy). Must
             be off any systemic corticosteroids for the treatment of brain metastases for at least
             14 days prior to enrollment.

          -  Patient has had a prescription or non-prescription drugs or other products known to be
             sensitive to CYP3A4 substrates or CYP3A4 substrates with a narrow therapeutic index,
             or to be moderate to strong inhibitors/inducers of CYP3A4 which cannot be discontinued
             2 weeks prior to day -3 of dosing and withheld throughout the study until 2 weeks
             after the last dose of study drug. Co-administration of aprepitant or fosaprepitant
             during this study is prohibited.

          -  Herbal preparations are not allowed throughout the study. These herbal medications
             include but are not limited to: St. John's wort, kava, ephedra (mahung), gingko
             biloba, dehydroepiandrosterone (DHEA), yohimbe, saw palmetto and ginseng. Patients
             should stop using these herbal medications 7 days prior to first dose of study
             treatment.

          -  Any known hypersensitivity or contraindication to the components of the study drug
             AZD1775 or olaparib.

          -  Any of the following cardiac diseases currently or within the last 6 months as defined
             by New York Heart Association (NYHA) >= class 2. a. Unstable angina pectoris; b.
             Congestive heart failure; c. Acute myocardial infarction; d. Conduction abnormality
             not controlled with pacemaker or medication; e. Significant ventricular or
             supraventricular arrhythmias (patients with chronic rate- controlled atrial
             fibrillation in the absence of other cardiac abnormalities are eligible).

          -  AZD1775 should not be given to patients who have a history of Torsades de pointes
             unless all risk factors that contributed to Torsades have been corrected. AZD1775 has
             not been studied in patients with ventricular arrhythmias or recent myocardial
             infarction.

          -  Patients with resting corrected QT interval (specifically QTc calculated using the
             Fridericia formula [QTcF]) > 470 msec from a single electrocardiogram (ECG) performed
             at study entry or congenital long QT syndrome.

          -  Pregnant or breast-feeding.

          -  Serious active infection at the time of study entry, or another serious underlying
             medical condition that would impair the ability of the patient to receive study
             treatment.

          -  Presence of other active invasive cancers.

          -  Psychological, familial, sociological, or geographical conditions that do not permit
             compliance with protocol.

          -  Patients with myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) or with
             features suggestive of MDS/AML.

          -  Previous allogenic bone marrow transplant or double umbilical cord blood
             transplantation (dUCBT).