This chapter, authored by David J. Aldous, aims to provide a comprehensive overview of exchangeability and related topics, particularly focusing on results from the post-1970 era. The introduction highlights the common perception that de Finetti's theorem, which states that an infinite exchangeable sequence can be derived from a random distribution, is the primary understanding of exchangeability. However, the author emphasizes the need to explore more recent developments in the field. The chapter is structured into several parts, with Part I delving into the central ideas surrounding de Finetti's theorem, while Part II presents complementary results, including Dacunha-Castelle's "spreading-invariance" property and Kallenberg's stopping time property, which provide alternative conditions equivalent to exchangeability. Additionally, Kingman's "paintbox" description of exchangeable random partitions is discussed, leading to Cauchy's formula for the distribution of certain random variables. The chapter is designed to be accessible to students with a standard graduate-level understanding of measure-theoretic probability theory, though some sections require knowledge of weak convergence.This chapter, authored by David J. Aldous, aims to provide a comprehensive overview of exchangeability and related topics, particularly focusing on results from the post-1970 era. The introduction highlights the common perception that de Finetti's theorem, which states that an infinite exchangeable sequence can be derived from a random distribution, is the primary understanding of exchangeability. However, the author emphasizes the need to explore more recent developments in the field. The chapter is structured into several parts, with Part I delving into the central ideas surrounding de Finetti's theorem, while Part II presents complementary results, including Dacunha-Castelle's "spreading-invariance" property and Kallenberg's stopping time property, which provide alternative conditions equivalent to exchangeability. Additionally, Kingman's "paintbox" description of exchangeable random partitions is discussed, leading to Cauchy's formula for the distribution of certain random variables. The chapter is designed to be accessible to students with a standard graduate-level understanding of measure-theoretic probability theory, though some sections require knowledge of weak convergence.