I. To establish whether E7389 (eribulin mesylate) can be given safely to patients with moderate and severe renal dysfunction at 1.4 mg/m^2/week (the maximum tolerated dose [MTD] previously defined for patients with normal renal function) on days 1 and 8 of a 21-day cycle. (Phase I) II. To characterize the pharmacokinetic (PK) profile of E7389 in patients with moderate and severe renal dysfunction. (Phase I) III. To determine the response rate of patients with advanced urothelial carcinomas to E7389 in the first-line setting. (Phase II) IV. To determine the 6-month, progression-free survival and overall survival of patients with advanced urothelial carcinomas treated with E7389. (Phase II) V. To document the toxicity associated with the administration of E7389 to patients with advanced urothelial carcinoma patients and varying degrees of renal dysfunction. (Phase II) VI. To determine the response rate of patients with advanced urothelial carcinomas to E7389 in the setting of progression after prior platinum-based chemotherapy for advanced or recurrent disease, in two cohorts: tubulin-inhibitor treated or tubulin-inhibitor naive. (Tubulin inhibitors in common use for urothelial cancer include paclitaxel, docetaxel and vinblastine). (Phase II) VII. To determine the 6-month progression-free survival and overall survival of patients with advanced urothelial carcinomas treated with E7389 after platinum-based therapy for recurrent or advanced disease. (Phase II) VIII. To document the toxicity associated with the administration of E7389 to patients with advanced urothelial carcinoma patients in the second line and later setting. (Phase II) IX. To compare men and women with advanced bladder cancer treated with E7389 with respect to toxicity of E7389 as classified by Common Terminology Criteria for Adverse Events (CTCAE) version (v)4 for (i) all hematologic toxicities, (ii) all non- hematologic toxicities, and (iii) the most frequently observed toxicities (neutropenia, anemia, leucopenia, infection). (Enrollment to additional females) X. To compare men and women with advanced bladder cancer treated with E7389 with respect to response to E7389 as evidenced by (i) disease control rate (DCR) defined as stable disease (SD)+partial response (PR)+complete response (CR) at 12 weeks, (ii) progression-free survival (PFS), and (iii) overall survival (OS). (Enrollment to additional females) XI. To compare men and women with advanced bladder cancer treated with E7389 with respect to pharmacokinetics of E7389. (Enrollment to additional females) XII. To compare men and women with advanced bladder cancer treated with E7389 with respect to tumoral expression of genes involved in the mechanism of action of E7389, including tubulin isotypes, microtubule-associated protein 4 (MAP4), and stathmin. (Enrollment to additional females)