Critical infrastructure is vulnerable to systemic long-term stressors such as climate change, as well as shocks from extreme weather events, economic disruptions, and cyber failures. The complexity and interdependencies across critical infrastructure domains makes it susceptible to cascading failures, with the SARS-CoV-2 pandemic is the most recent example of disruptions in supply chains, healthcare and emergency facilities. Stress testing offers a conceptual framework and methodology for identifying risks associated with cascading failures and selecting mitigation and recovery strategies. This paper reviews the fundamentals of stress-testing science and practice in different fields (medicine, engineering, economics) and identifies challenges associated with the application of existing methodologies to infrastructure systems. The currently practiced risk-based stress testing approaches may only be of limited use because they merely aim to identify the components of failing systems by varying stress loads. Adding a systems-thinking perspective and consideration of interconnectedness across system domains facilitates resilience stress testing (i.e., the impact of disruptions on the system's ability to recover and adapt). We propose combining risk and resilience stress testing into a tiered approach applicable to complex, interconnected infrastructure.