Inclusion Criteria:
* Patients must have metastatic histologically or cytologically confirmed uveal melanoma. (If histologic or cytologic confirmation of the primary is not available, confirmation of the primary diagnosis of uveal melanoma by the treating investigator can be clinically obtained, as per standard practice for uveal melanoma). Pathologic confirmation of diagnosis will be performed at Columbia University, Memorial Sloan-Kettering Cancer Center (MSKCC) or Vanderbilt University Medical Center
* Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1
* Age \>= 18 years. Because limited dosing or adverse event data are currently available on the use of vorinostat in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric single-agent trials, if applicable
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Life expectancy of greater than 3 months
* Leukocytes \>= 3,000/mcL
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Hemoglobin \>= 9.0 g/dL not requiring transfusions within the past 2 weeks
* Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN); =\< 3 x institutional ULN if the patient has Gilbert's syndrome
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN if no liver metastasis present; =\< 5 x institutional ULN if liver metastases are present
* Creatinine =\< 1.5 mg/dL
* Ability to understand and the willingness to sign a written informed consent document
* Vorinostat is toxic to the developing human fetus. For this reason and because Class D agents are known to be teratogenic, women of child-bearing potential and men must agree to use effective 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 she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of vorinostat administration
Exclusion Criteria:
* Patients may have had any number of prior therapies. At least 3 weeks must have elapsed since the last dose of systemic therapy. At least 6 weeks must have elapsed if the last regimen included BCNU or mitomycin C. At least 6 weeks must have elapsed if the last regimen included an anti-CTLA4 antibody. Patients must have experienced disease progression on their prior therapy in the opinion of the treating investigator
* Patients who are receiving any other investigational agents
* Patients with active or untreated brain metastases. Treated brain metastases must have been stable for at least 2 months
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to vorinostat
* Patients receiving HDAC inhibitors or compounds with HDAC inhibitor like activity, such as valproic acid, are ineligible. Patients who have received such agents may enroll on this study after a 14-day washout period
* Patients on warfarin will be excluded from the trial if they cannot be switched to an acceptable alternative medication (i.e. low molecular weight heparin \[LMWH\]). Prolongation of prothrombin time (PT) and International Normalized Ratio (INR) were observed in patients receiving vorinostat concomitantly with coumarin-derivative anticoagulants
* Pregnant women are excluded from this study because vorinostat is a Class D agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with vorinostat, breastfeeding should be discontinued if the mother is treated with vorinostat
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy will be eligible unless the CD4 count is \< 200 cells/mm\^3 within one month of study enrollment (as requested by Cancer Therapy Evaluation Program \[CTEP\]). These patients are at increased risk of lethal infections when treated with marrow-suppressive therapy
* A second malignancy requiring active therapy
* No concomitant anti-cancer chemotherapy or other systemic drugs. Palliative radiation therapy will be allowed as long as the patient meets all other eligibility criteria
* Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g., inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption
* Corrected QT interval (QTc) \> 475 milliseconds
* Patients who cannot swallow capsules
