A set of integers is called Sidon if any continuous function on the unit circle with spectrum in the set has an absolutely convergent Fourier series. We will recall some of the classical theory of Sidon sets of integers, or more generally of characters on compact groups (Abelian or not). We will then give several recent extensions to Sidon sets, randomly Sidon sets and subgaussian sequences in bounded orthonormal systems, following recent work by Bourgain and Lewko, and by the author, both currently available on arxiv.