Trait-based approaches focus on the functional traits that define how organisms interact with the environment and each other. They represent an efficient way to capture different aspects of diversity in ecological models, which is essential for understanding community structure and ecosystem functioning, both now and in the future. There is an extensive history of trait-based approaches in theoretical ecology, enriched by an expanding array of complementary frameworks. In this chapter, we give a pedagogical introduction to one such framework—adaptive dynamics—explaining how to both set up and analyse models and surveying a range of applications. Then we show how adaptive dynamics relates to other frameworks, including species sorting, ecological quantitative genetics, and moment methods, highlighting the differences and connections between them. We then consider how these basic theories can be extended to incorporate temporal and spatial heterogeneity and multiple traits. Finally, we outline some frontiers of trait-based theory, including connections with empirical systems, linking trait- and species-based approaches, and embedding trait-based approaches in Earth system models.