Constraining extended scalar sectors at current and future colliders -- an update

In this proceeding, I discuss several models that extend the scalar sector of the Standard Model by additional matter states. I here focus on results for models with singlet extensions, which have been obtained recently and update some of the results presented in previous work. In more detail, I will briefly review the option to test a strong first-order electroweak phase transition using precision measurements in the electroweak sector, as well as production cross-sections for non-standard scalar production at Higgs factories.