The discovery and study of the Higgs boson at the Large Hadron Collider of CERN has proven the validity of the Brout–Englert–Higgs mechanism of mass creation in the standard model via spontaneous symmetry breaking. The new results obtained by the ATLAS and CMS Collaborations at the LHC show that all measured cross-sections agree within uncertainties with the predictions of the theory. However, the standard model has obvious difficulties (nonzero neutrino masses, hierarchy problem, existence of dark matter, non-existence of antimatter galaxies, etc.), which point towards more possible violated symmetries. We first summarize the present status of the studies of the Higgs boson, including the latest results at 13 TeV p-p collision energy, then enlist some of the problems with possible solutions and the experimental situation regarding them.