Cediranib Maleate in Treating Patients With Persistent, Recurrent, or Refractory Advanced Ovarian Epithelial, Peritoneal Cavity, or Fallopian Tube Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed epithelial ovarian cancer, fallopian tube cancer, or primary peritoneal cancer that has recurred or is refractory to initial therapy; patients must have received platinum-based chemotherapy before entry into this protocol * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> 20 mm with conventional techniques or as \> 10 mm with spiral computed tomography (CT) scan OR patients must have evidence of progression based on an elevated CA-125 (defined as a value of \> 2 x upper limit of normal \[ULN\] documented on two separate determinations made \> 2 weeks apart) if the physical exam is normal and CT scan of the chest/abdomen/pelvis, has a disease volume \< 1 cm in maximum diameter * Patients may have received no more than one prior chemotherapy regimen (i.e. initial first-line chemotherapy only) * Life expectancy of greater than 12 weeks * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 8 g/dL * Total bilirubin within normal institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 × institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Women of child-bearing potential must have a negative pregnancy test prior to study entry; 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 and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, radiotherapy, or major surgery 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 * Patients with borderline tumors or tumors of low malignant potential * Patients with current bowel obstruction * Patients may not be receiving any other investigational agents nor have participated in an investigational trial within the past 30 days * Patients with known brain metastases should be excluded from this clinical trial * History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD2171 (cediranib maleate) * Mean corrected QT (QTc) \> 470 msec (with Bazett's correction) in screening electrocardiogram or history of familial long QT syndrome * Greater than +1 proteinuria on two consecutive dipsticks taken no less than 1 week apart * Uncontrolled intercurrent illness including, but not limited to hypertension, 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 AZD2171 * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible * Any significant abnormality noted in the electrocardiogram (ECG) within 14 days of treatment * A New York Heart Association classification of III or IV (NOTE: patients classified as class II controlled with treatment may continue with increase monitoring) * Conditions requiring concurrent use of drugs or biologics with proarrythmic potential; these drugs are prohibited during studies with AZD2171