Pembrolizumab and Docetaxel or Gemcitabine Hydrochloride in Treating Patients Urothelial Cancer

Inclusion Criteria: * Have locally advanced or metastatic urothelial cancer that is not amenable to curative surgical treatment * Have histologically or cytologically confirmed urothelial tract carcinoma * Be previously chemotherapy-treated; all patients may have received up to two prior lines of chemotherapy (excludes systemic therapy) for recurrent/advanced disease, as long as one of those regimens was platinum-based; (it is anticipated that patients would have been previously treated with MVAC or GC, or variations of these standard frontline regimens) * Be willing and able to provide written informed consent for the trial * Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 * Have provided tissue from an archival tissue sample or newly obtained core or excisional biopsy of a tumor lesion * Life expectancy of greater than 6 months * Have a performance status of 0 to 1 on the Zubrod performance scale * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL or \>= 5.6 mmol/L * Serum creatinine =\< 1.5 X upper limit of normal (ULN) OR measured or calculated\* creatinine clearance \>= 60 mL/min for subject with creatinine levels \> 1.5 X institutional ULN; (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance \[CrCl\]) * Creatinine clearance should be calculated per institutional standard * Serum total bilirubin =\< 1.5 X ULN OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN OR =\< 5 X ULN for subjects with liver metastases * Alkaline phosphatase not applicable (N/A) * International normalized ratio (INR) or prothrombin time (PT) =\<1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants * Activated partial thromboplastin time (aPTT) =\< 1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication; subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy Exclusion Criteria: * Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment * Has known hypersensitivity to MK-3475 (pembrolizumab) or any of its incipients * Patients with a known hypersensitivity to gemcitabine (Arm B only) * Patients with hypersensitivity to docetaxel or polysorbate 80 (Arm A only) * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has had a prior monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent * Note: Subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study * Note: If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy * Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy; free of disease for more than 5 years * Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis; subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment * Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment; anti-coagulants are permitted * Has evidence of interstitial lung disease or active, non-infectious pneumonitis * Has an active serious bacterial infection requiring systemic antimicrobial therapy * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment * Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-cluster of differentiation (CD)137, or anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways) * Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies) * Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected) * Has received a live vaccine within 30 days prior to the first dose of trial treatment