When the CMS and ATLAS experiments at the CERN Large Hadron Collider (LHC) announced the discovery the Higgs Boson in July of 2012, this completed what is known as the Standard Model (SM) of particle physics. However, it was already apparent that there were phenomena in nature that were not explained by the SM and that additional physics "beyond the Standard Model (BSM)" was needed. There is reason to believe that some of the BSM physics will be accessible with more data at the LHC.  After describing the LHC and the CMS detector, I will discuss recent results from CMS on the search for physics beyond the SM; prospects for the data-taking period that is just starting and will last for about two more years; CERN's plan to increase the LHC luminosity (collision rate) far beyond its initial design; and the CMS collaboration's plans to upgrade the detector to handle the higher rates.