• Patients must have histologically confirmed recurrent platinum-resistant epithelial ovarian carcinoma (EOC) of any histology, as defined by progression within 6 months of the last dose of platinum-based chemotherapy. Both primary platinum resistant and acquired platinum resistant patients are allowed

• High-grade serous histology is required (for the dose expansion cohort only) (data on BRCA (e.g. germline BRCA, Somatic BRCA, Neither, Unknown) and homologous recombination deficiency (HRD)/Loss of Heterozygosity (LOH) (e.g. HRD \> 42/LOH \>16%, HRD score \< 42/LOH \< 16%, Unknown) is not required for study but will be collected if available

• Patients must have received 1-3 prior systemic therapies

• Women age \>= 18 years. Because no dosing or adverse event data are currently available on the use of abemaciclib in combination with olaparib in patients \<18 years of age, children are excluded from this study

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)

• Hemoglobin \>= 10 g/dL (within 28 days prior to administration of study treatment)

‣ Patients may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the investigator. Initial treatment must not begin earlier than the day after the erythrocyte transfusion

• Absolute neutrophil count \>= 1,500/mcL (within 28 days prior to administration of study treatment)

• Platelets \>= 100,000/mcL (within 28 days prior to administration of study treatment)

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (within 28 days prior to administration of study treatment)

‣ Patients with Gilbert's syndrome with a total bilirubin =\< 2.0 times ULN and direct bilirubin within normal limits are permitted

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) / alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 3 x institutional ULN, unless liver metastases are present in which case they must be =\< 5 x ULN (within 28 days prior to administration of study treatment)

• Patients must have creatinine clearance estimated of \>= 51 mL/min using the Cockcroft-Gault equation or based on a 24-hour urine test (within 28 days prior to administration of study treatment)

• Glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2 (within 28 days prior to administration of study treatment). Estimated GFR calculated using Cockcroft-Gault equation

• Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial

• For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

‣ Active hepatitis B virus (HBV) is defined by a known positive HBV surface antigen (HBsAg) result. Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody and absence of HBsAg) are eligible

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.

‣ Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV ribonucleic acid (RNA)

• Patients with treated brain metastases are eligible if patient is stable for at least 4 weeks status post (s/p) radiation therapy and off corticosteroids, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\] scan) during the screening period

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better

• Postmenopausal or evidence of non-childbearing status, a negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1. Postmenopausal is defined as:

‣ Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments

⁃ Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the postmenopausal range for women under 50

⁃ Radiation-induced oophorectomy with last menses \> 1 year ago

⁃ Chemotherapy-induced menopause with \> 1 year interval since last menses

⁃ Surgical sterilization (bilateral oophorectomy or hysterectomy)

• The effects of abemaciclib and olaparib on the developing human fetus are unknown. For this reason and because CDK-and PARP-inhibiting agents are known to be teratogenic, women of child-bearing potential and their partners, who are sexually active, must agree to the use of one highly effective form of contraception and their partner must use a male condom prior to study entry, for the duration of study participation, and for 6 months after the last dose of study treatment. 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

• For the dose expansion cohort, patients must have disease amenable to biopsy for correlative studies, specifically at least 1 tumor accessible and safe for biopsy on office exam or tumor that a radiologist deems is safe for biopsy in interventional radiology department based on imaging (dose expansion cohort only). For the dose escalation cohort, patients with evaluable disease are acceptable

• For inclusion in i) the optional genetic research and ii) the optional biomarker research, patients must fulfill the following criteria:

‣ Provision of informed consent for genetic research prior to collection of sample

⁃ Provision of informed consent for biomarker research prior to collection of sample

⁃ If a patient declines to participate in the optional exploratory genetic research or the optional biomarker research, there will be no penalty or loss of benefit to the patient. The patient will not be excluded from other aspects of the study

• Patients may not have received prior CDK 4/6 inhibitors. Previous PARP inhibitor use is allowed in front-line treatment but not for recurrent disease

• Patients who received chemotherapy must have recovered (Common Terminology Criteria for Adverse Events \[CTCAE\] grade =\< 1) from the acute effects of chemotherapy except for residual alopecia or grade 2 peripheral neuropathy prior to randomization. A washout period of at least 21 days is required between last chemotherapy dose and randomization (provided the patient did not receive radiotherapy)

• Patients who received radiotherapy must have completed and fully recovered from the acute effects of radiotherapy. A washout period of at least 28 days is required between end of radiotherapy and randomization

• For agents other than chemotherapy, a 4 week washout period is required. Previous bevacizumab use is allowed

• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible