Resectable gastric or gastroesophageal (G/GEJ) cancer is a heterogeneous disease with no defined molecularly based treatment strategy. Unfortunately, nearly half of patients experience disease recurrence despite standard treatments (neoadjuvant and/or adjuvant chemotherapy/chemoradiotherapy and surgery). In this review, we summarize the evidence of potential tailored approaches in perioperative treatment of G/GEJ cancer, with a special focus on patients with human epidermal growth factor receptor-2(HER2)-positive and microsatellite instability-high (MSI-H) tumors. In patients with resectable MSI-H G/GEJ adenocarcinoma, the ongoing INFINITY trial introduces the concept of non-operative management for patients with complete clinical-pathological-molecular response, and this could be a novel and potential practice changing strategy. Other pathways involving vascular endothelial growth factor receptor (VEGFR), fibroblast growth factor receptor (FGFR), claudin18 isoform 2 (CLDN18.2), and DNA damage repair proteins are also described, with limited evidence until now. Although tailored therapy appears to be a promising strategy for resectable G/GEJ cancer, there are several methodological issues to address: inadequate sample size for pivotal trials, underestimation of subgroup effects, and choice of primary endpoint (tumor-centered vs. patient-centered endpoints). A better optimization of G/GEJ cancer treatment allows maximizing patient outcomes. In the perioperative phase, although caution is mandatory, times are changing and tailored strategies could introduce new treatment concepts. Overall, MSI-H G/GEJ cancer patients possess the characteristics to be the subgroup that could receive the most benefit from a tailored approach.