Higgs Physics at CMS

The discovery of the Standard Model Higgs boson performed by the CMS and ATLAS collaborations during the LHC Run 1 has been an important success. This document is a short review of the search for the Higgs boson performed by the CMS collaboration during the LHC Run 1 and Run 2. In the first part, after a brief description of the Higgs boson production and decay channels, the Run-1 results are presented emphasizing the possible hints of New Physics. The main part of this document is devoted to the search for the Higgs boson with the 13 TeV data collected by the CMS experiment in 2015 and 2016, including the Standard Model searches as well as the Beyond Standard Model searches, such as the search for additional Higgs bosons and for resonant and non-resonant double Higgs boson production