Inclusion Criteria:  Pathologically confirmed locally advanced or metastatic urothelial carcinoma by histology Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 Not eligible to receive cisplatin-based chemotherapy due to renal dysfunction (defined as creatinine clearance [CrCl] =< 60 mL/min), > grade 2 peripheral neuropathy, or ototoxicity (defined as >= grade 2 hearing loss); OR unwillingness of patient to receive cisplatin; OR progressed on one platinum-based chemotherapy regimen for advanced disease May have had neoadjuvant or adjuvant platinum-based chemotherapy or intravesical therapy in the past >= 18 years of age Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1 or 2 Life expectancy >= 3 months Absolute neutrophil count (ANC) >= 1.5 × 10^9/L Platelet count >= 100 × 10^9/L Hemoglobin >= 9 g/dL (may have been transfused) Total bilirubin level =< 1.5 x the upper limit of normal (ULN) range (except patients with Gilbert's syndrome who must have a total bilirubin of < 3 x ULN) Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels =< 2.5 x ULN, or AST and ALT levels =< 5 x ULN (for subjects with documented metastatic disease to the liver) Creatinine clearance >= 30 mL/min by Cockcroft-Gault formula Subjects with active hepatitis B virus (Hep B) are allowed if antiviral therapy for hepatitis B has been given for > 8 weeks and viral load is < 100 IU/mL prior to first dose of trial treatment. Subjects with untreated hepatitis C virus (HCV) are allowed. Subjects with human immunodeficiency virus (HIV) who have CD4+ T-cell counts >= 350 cells/uL and no history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections in the last year are allowed Willingness to undergo mandatory pre-treatment biopsy (unless there is adequate archival tumor specimen available for PD-L1 IHC evaluation) Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for >= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy). Or, female subjects of childbearing potential must have a negative serum or urine pregnancy test within 72 hours prior to the first study drug administration Male and female subjects who are of reproductive potential must agree to use highly effective method of birth control (e.g., implants, injectables, birth control pills with two hormones, intrauterine devices [IUDs], complete abstinence or sterilized partner, and female sterilization) and a barrier method (e.g., condoms, vaginal ring, sponge, etc.) during the period of therapy and for 4 months after the last dose of study drug Ability to understand and willingness to sign an informed consent form Ability to adhere to the study visit schedule and other protocol requirements Must be able to swallow study drug  Exclusion Criteria:  Receiving radiation =< 14 days prior to enrollment to the site of selected target lesions Systemic therapy for cancer =< 21 days prior to enrollment Autoimmune disorder requiring active therapy as defined by corticosteroids at a dose >= 10 mg oral prednisone or the equivalent or requiring chronic immunosuppressive therapy Use of corticosteroids =< 14 days prior to enrollment at a dose of >= 10 mg oral prednisone or the equivalent per day Received immune checkpoint inhibitor therapy (anti-PD-1, anti-PD-L1, or anti-CTLA4 directed therapy) on a prior clinical trial Has received selinexor or another XPO1 inhibitor previously Any active gastrointestinal dysfunction that could interfere with absorption of study treatment in the opinion of the investigator Pregnant or lactating women Any condition that would prohibit the understanding or rendering of informed consent Any condition including additional malignancies, laboratory abnormalities, or psychiatric illness that in the opinion of the investigator would interfere with the patient's safety or compliance while on trial Severe infection that in the opinion of the investigator would interfere with patient safety or compliance on trial within 4 weeks prior to enrollment