Addressing the global challenges of climate change and biotic invasions requires understanding their interactions and implications for natural resource management. To facilitate and support invasive species management in a changing climate, we review how climate change and invasions interact to impact the planning, action, and outcomes of invasive species management. Climate change is facilitating the introduction of new potential invasive species and altering pathways of introduction and spread, with implications for which species natural resource managers need to assess, monitor, and target. Climate‐driven shifts in invasive species phenology require more flexible management timelines. Climate change may reduce the efficacy and feasibility of current treatment methods and make native ecosystems more vulnerable to invasion. Additionally, disturbance caused by extreme climate events can compound the spread and impacts of biological invasions, making invasive species management a necessary part of extreme event preparation and response planning. As a solution to these challenges, we propose climate‐smart invasive species management, which we define as the approaches that managers and decision‐makers can take to address the interactive effects of climate change and invasions. Climate‐smart invasive species management includes considering potential shifts in species ranges, abundances, and impacts to inform monitoring, treatment, and policies to prevent new invasive species. Climate‐smart management may also involve adjusting the timing and type of treatment to maintain efficacy, promoting resilient ecosystems through climate‐smart restoration, and considering the effects of climate change when setting management goals. Explicitly considering the interactions of climate change and biological invasions within organizational decision‐making and policy can lead to more effective management and promote more resilient landscapes.