Self-interacting dark matter has been the subject of increasing interest in recent years, motivated partially by the reported small-scale discrepancies between astrophysical observations and the cosmologicalconcordance model. In this context, an attractive way to achieve both strong, velocity-dependent self-interactions and thermal production is to couple dark matter to light new particles. I will discuss model-building avenues and the resulting phenomenology, with a particular focus on recently derived strong constraints on such models from the Cosmic Microwave Background and other indirect detection probes.