The challenges posed by multi‐crisis environments, such as pandemics and geopolitical uncertainties, create significant opportunities for supply chains (SC) to enhance their sustainability, resilience, and agility, thereby developing a strategic advantage. However, seizing these opportunities is not without its challenges; critical tensions inevitably arise. This paper, based on a systematic review of 287 SC studies, identifies and discusses five key tensions: (1) increased trade‐offs between sustainability and efficiency; (2) competing priorities between SC sustainability and resilience; (3) mismatched sustainability expectations causing stakeholder pressure; (4) conflicting demands between global and sustainable operations; and (5) unintended consequences of technological innovation, disadvantaging stakeholders with limited resources and capabilities. To mitigate these tensions while leveraging on the opportunities, the study proposes several strategic pathways, including adopting circular economy principles, optimizing inventory and distribution management, employing holistic measurement and forecasting, balancing risk‐hedging with proactive risk management, fostering inclusive stakeholder engagement, balancing globalization and regionalization, and integrating advanced digital technologies alongside with SC ecosystem wide change management. These strategies offer practical guidance for building sustainable and crises‐ready SCs and set the stage for an extensive research agenda to further explore SC sustainability in multi‐crisis environments.