Is the newly discovered Higgs boson alone, or is it a member of an extended family of scalar particles? To what extent will it be possible to answer this question by means of the experimental progress of the coming years? I will address this issue in the simple, yet phenomenologically relevant scenario where the standard Higgs boson mixes with a scalar singlet. First I will quantify the current constraints from direct searches for the extra scalar state, as well as the indirect ones coming from the measurement of the Higgs couplings. I will then consider the prospects for these searches at future hadron and lepton colliders (different stages of the LHC, ILC, FCC). In particular, the projected reaches of direct searches at future machines are obtained extrapolating the present LHC results with a technique that I will discuss. The results are first presented in a model-independent way, in a generic extension of the Standard Model with a scalar singlet, and then specified to a few most natural models: the NMSSM, Twin Higgs, and composite Higgs.