Function-valued traits—phenotypes whose expression depends on a continuous index (such as age, temperature, or space)—occur throughout biology and, like any trait, it is important to understand how they vary and evolve. Although methods for analyzing variation and evolution of function-valued traits are well developed, they have been underutilized by evolutionists, especially those who study natural populations. We seek to summarize advances in the study of function-valued traits and to make their analyses more approachable and accessible to biologists who could benefit greatly from their use. To that end, we explain how curve thinking benefits conceptual understanding and statistical analysis of functional data. We provide a detailed guide to the most flexible and statistically powerful methods and include worked examples (with R code) as supplemental material. We review ways to characterize variation in function-valued traits and analyze consequences for evolution, including constraint. We also discuss how selection on function-valued traits can be estimated and combined with estimates of heritable variation to project evolutionary dynamics.