Estimates of changes in the frequency or height of contemporary extreme sea levels (ESLs) under various climate change scenarios are often used by climate and sea level scientists to help communicate the physical basis for societal concern regarding sea-level rise. Changes in ESLs (i.e., the hazard) are often represented using various metrics and indicators that, when anchored to salient impacts on human systems and the natural environment, provide useful information to policy makers, stakeholders, and the general public. While changes in hazards are often anchored to impacts at local scales, aggregate global summary metrics generally lack the context of local exposure and vulnerability that facilitates translating hazards into impacts. Contextualizing changes in hazards is also needed when communicating the timing of when projected ESL frequencies cross critical thresholds, such as the year in which ESLs higher than the design height benchmark of protective infrastructure (e.g., the 100-yr water level) are expected to occur within the lifetime of that infrastructure. We present specific examples demonstrating the need for such contextualization using a simple flood exposure model, local sea-level rise projections, and population exposure estimates for 414 global cities. We suggest regional and global climate assessment reports integrate global, regional, and local perspectives on coastal risk to address hazard, vulnerability and exposure simultaneously.