Climate change creates new challenges for those who design, manage, and use infrastructure. There is increasing evidence that our civil infrastructure are vulnerable to climate change. We start by summarizing the evidence for how infrastructure are vulnerable to climate change hazards (including heat, precipitation, wildfires, and flooding). We focus on power, water, and transportation systems but discuss generalizable challenges for any major infrastructure. Next, we discuss how the interdependencies between infrastructure systems create challenges for mitigating climate change vulnerabilities. To date, infrastructure have largely been planned to withstand particular design storms, or environmental hazards that occur with a particular frequency and intensity (e.g., the 100 year storm). We discuss the challenges of this risk-based approach in a future marked by climate non-stationarity and the need for resilience-based design and operation that embraces this uncertainty. Given that infrastructure are long-lasting and climate is changing quickly, we describe the need for agile and flexible infrastructure as central to resilience strategies.