One of the major physics goals of the CMS experiment at the LHC is the measurement of the 125 GeV Higgs boson's couplings to known standard model particles. Since the same coupling can contribute to several different Higgs production and decay processes, the most precise and model independent determination comes from a combined global fit to all of the available data. I will discuss the recent combined measurements and interpretations from the CMS experiment using the full 2016 dataset, corresponding to 35.9 fb-1 of integrated luminosity. In addition to testing the data's compatibility with the standard model predictions, I will also discuss how these measurements constrain indirectly BSM physics, in particular models with extended Higgs sectors and those that predict exotic Higgs decays. Finally I will discuss a "road map" for how these measurements will evolve in the era of the HL-LHC, using as a first example the recent CMS combined measurements of differential Higgs production cross sections.