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 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
* All patients may have received up to two prior lines of chemotherapy for recurrent/advanced disease
* Patients must have received at least one platinum-based chemotherapy for recurrent/advanced disease; recurrent disease is defined as having recurred after definitive therapy and advanced disease is defined as T4 and/or N2 and/or M1; in addition, for completion of Cohort #2, patients must also have received a tubulin inhibitor as part of their therapy for urothelial cancer; for purposes of this evaluation, treatment with chemotherapy regimens where carboplatin or similar is substituted for cisplatin or where a taxane is added or removed will be considered the same regimen; tubulin inhibitors in common use include paclitaxel, docetaxel, and vinblastine; the exception to this requirement applies to women
* Women with and without prior therapy are also eligible; priority will be given to those who consent to participating in the pharmacokinetic studies
* Life expectancy of greater than 6 months
* Eastern Cooperative Oncology Group (ECOG) performance status 0-2 and Karnofsky >= 60%
* Absolute neutrophil count >= 1,000/mcL
* Platelets >= 100,000/mcL
* Hemoglobin >= 9 g/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
* Patients must have either (a) normal kidney function (i.e. creatinine =< 1.5 X upper limit of normal \[ULN\] OR calculated creatinine clearance >= 60 mL/min by the modified Cockcroft and Gault Formula OR a creatinine clearance >= 60 mL/min obtained from a 24-hour urine collection) or (b) moderate or severe renal dysfunction (i.e. creatinine clearance < 60 mL/min and >= 20 mL/min)
* Patients with symptomatic uremia, uncontrolled edema or unstable serum electrolytes should not enter the trial until such time as they have been stabilized - such patients should be discussed with the principal investigator
* Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of E7389 Halichondrin analog will be determined following review of their case by the principal investigator
* The effects of E7389 Halichondrin analog on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because tubulin inhibitors are known to be teratogenic, 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 brain metastasis that are unstable (i.e. presenting with neurologic symptoms that progress or require increasing doses of steroids within a 4-week period) or are untreated (i.e. not radiated) should be excluded
* Uncontrolled intercurrent illness including, but not limited to, 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 because E7389 Halichondrin analog is tubulin inhibitor 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 E7389 Halichondrin analog, breastfeeding should be discontinued if the mother is treated with E7389
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with E7389 Halichondrin analog; HIV-positive patients with CD4+ =< 500/mm3 are ineligible because they are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in this group of patients when indicated
* Prior therapy with E7389 Halichondrin analog (eribulin)