This is a two arm Phase III trial in first and second-line HER2 negative patients with locally recurrent or metastatic breast cancer. The primary endpoint is overall survival (OS), and the objective is to test for the superiority of eribulin mesylate over standard weekly paclitaxel. Patients will be randomized between the experimental and control arm with equal allocation (1:1) within strata defined by prior adjuvant taxanes, hormone receptor status, and line of therapy. Subjects will continue protocol directed therapy until documentation of disease progression, development of unacceptable toxicity, or withdrawal of consent. Those who discontinue study treatment without radiological progression will be followed with repeat imaging studies every 12 weeks. All subjects will be followed until death, withdrawal of consent, or study termination.