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According to the tests that are in the reach of the ATLAS and CMS experiments, the recently discovered H boson has properties that are similar to those of a Standard Model (SM) scalar boson. Still, the observation of some SM properties, as well as searches for deviations from the SM or direct searches for exotic decays will either only become possible with more data, or will become increasingly sensitive. In addition, well-motivated extended scalar sectors are not excluded by data yet. I will present recent results from the CMS experiment on the measurements of processes involving the H boson, and discuss the present state of knowledge of the H boson properties. I will also present results of searches for beyond-the- SM scalar bosons, and prospects for the high-luminosity HL-LHC running.