Composite Higgs models offer a valid alternative to the Standard Model Higgs sector, where the electroweak symmetry breaking is explained naturally by non-perturbative dynamics. They also offer rich phenomenology that can be explored at the LHC and, more importantly, at future colliders. After a brief theoretical introduction to this class of models, I will discuss new features of these models that can be searched for at future colliders both via the precision and via the high-energy frontiers.