Resilience curves are used to communicate quantitative and qualitative aspects of system behavior and resilience to stakeholders of critical infrastructure. Generally, these curves illustrate the evolution of system performance before, during, and after a disruption. As simple as these curves may appear, the literature contains underexplored nuance when defining "performance" and comparing curves with summary metrics. Through a critical review of 273 publications, this manuscript aims to define a common vocabulary for practitioners and researchers that will improve the use of resilience curves as a tool for assessing and designing resilient infrastructure. This vocabulary includes a taxonomy of resilience curve performance measures as well as a taxonomy of summary metrics. In addition, this review synthesizes a framework for examining assumptions of resilience analysis that are often implicit or unexamined in the practice and literature. From this vocabulary and framework comes recommendations including broader adoption of productivity measures; additional research on endogenous performance targets and thresholds; deliberate consideration of curve milestones when defining summary metrics; and cautionary fundamental flaws that may arise when condensing an ensemble of resilience curves into an "expected" trajectory.