Extended Higgs sectors represent one of the main motifs in building bSM models and testing their collider and astroparticle consequences. The two-Higgs-doublet model (2HDM) was the main reference bSM model in the past decade. Now many theorists move to more complicated scalar sectors and discover phenomena which are impossible even within 2HDM. After a brief introduction into the history of multi-Higgs-doublet models, I will show several recent results on symmetries and CP properties in 3HDM, which are appealing theoretically and can lead to interesting phenomenological consequences.