The Large Hadron Collider (LHC) is getting ready to start run-II with proton-proton collisions at the increased centre of mass energy of 13 TeV, and a more detailed study of the properties of the Higgs particle, as well as the hunt for possible other Higgs bosons, is high on the physics program. In this lecture we give a review of the current understanding and most results of measurements of the Higgs boson by the CMS experiment, as well as the status of the searches for other Higgs bosons. A short outlook will be given on Higgs physics expected with the data of the next upcoming runs of the LHC.
