This two-cohort, open-label, multicenter study will assess the safety, efficacy and tolerability of trastuzumab emtansine in participants with HER2-positive locally advanced breast cancer (LABC) or metastatic breast cancer (mBC) who have received prior anti-HER2 and chemotherapy-based treatment. Participants in Cohort 1 will be drawn from the general participant population; Cohort 2 will include only Asian participants.