Trastuzumab, a monoclonal antibody to human epidermal growth factor receptor 2 (HER2), has improved survival in patients with HER2-positive advanced gastric or gastroesophageal junction cancer (AGC). The inevitable development of resistance to trastuzumab remains a problem, however, with several treatment strategies that have proven effective in breast cancer having failed to show clinical benefit in AGC. In this review, we summarize the mechanisms underlying resistance to HER2-targeted therapy and outline past and current challenges in the treatment of HER2-positive AGC refractory to trastuzumab. We further describe novel agents such as HER2 antibody–drug conjugates that are under development and have shown promising antitumor activity in early studies.