Inclusion Criteria:

          -  Patients must have locally advanced or metastatic urothelial cancer that is not
             amenable to surgical treatment

          -  Patients must have histologically or cytologically confirmed urothelial tract
             carcinoma; patients with urothelial carcinoma of the bladder, upper tract, or urethra
             are eligible

          -  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 for the evaluation of measurable disease (Response Evaluation Criteria in Solid
             Tumors version 1.1 [RECIST v1.1])

          -  Patients must have evidence of disease progression prior to enrollment

          -  All patients must have received a prior platinum-based chemotherapy regimen for
             treatment of urothelial cancer and must now be considered refractory to platinum-based
             chemotherapy; patients may have received the platinum-containing regimen either in the
             peri-operative or metastatic setting

          -  Patients may have received up to one line of prior systemic chemotherapy for
             recurrent/metastatic disease; if a platinum-based regimen was received both in the
             peri-operative setting and again in the metastatic setting, this will be considered 1
             line of chemotherapy

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0-1

          -  Absolute neutrophil count >= 1,000/mcL

          -  Platelets >= 100,000/mcL

          -  Hemoglobin >= 8.5g/dL

          -  Total bilirubin =< 1.5 institutional upper limit of normal (IULN)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT)(serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 X IULN

          -  Calculated creatinine clearance >= 30 mL/min by the modified Cockcroft and Gault
             Formula OR glomerular filtration rate >= 30 mL/min/body surface area (BSA) by
             Modification of Diet in Renal Disease or Chronic Kidney Disease Epidemiology
             Collaboration (CKD-EPI) formula

          -  Women and men of child-bearing potential 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

          -  Patients must have the ability to understand and the willingness to sign a written
             informed consent document

        Exclusion Criteria:

          -  Patients may not be receiving any other investigational agents

          -  Patients with untreated known brain metastases, or treated brain metastases that are
             clinically unstable

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, or
             psychiatric illness/social situations that would limit compliance with study
             requirements

          -  Women known to be pregnant

          -  Women who are breastfeeding and who are unwilling to stop breastfeeding prior to study
             entry

          -  Patients with known prior human immunodeficiency virus (HIV)-positive status on
             combination antiretroviral therapy are ineligible; known prior HIV-positive patients
             with CD4+ =< 500/mm^3 are ineligible (HIV testing is not required as part of this
             study)

          -  Pre-existing interstitial lung disease

          -  Inability to take oral medications

          -  Prior therapy with afatinib