  I review possible explanations of the muon g-2 anomaly in models with
extended Higgs and matter sectors, focusing on extensions of the standard model
and the two Higgs doublet model with vectorlike leptons. Predictions of these
models, namely the modifications of muon Yukawa and gauge couplings, that can
be searched for at the LHC and future colliders, are summarized. I also discuss
striking predictions for di-Higgs and tri-Higgs signals at a muon collider that
can be tested even at very low energies. Furthermore, I briefly comment on
other interesting features and signatures of models with extended Higgs sector
and vectorlike matter.
