  We make a substantially updated review and a systematic and comprehensive
analysis of the decays of Higgs bosons in the Standard Model (SM) and its three
well-defined prototype extensions such as the complex singlet extension of the
SM (cxSM), the four types of two Higgs-doublet models (2HDMs) without
tree-level Higgs-mediated flavour-changing neutral current (FCNC) and the
minimal supersymmetric extension of the SM (MSSM). We summarize the
state-of-art of theoretical predictions for the decay widths of the SM Higgs
boson and those appearing in its extensions taking account of all possible
decay modes. We incorporate them to study and analyze decay patterns of
CP-even, CP-odd, and CP-mixed neutral Higgs bosons and charged ones. We put
special focus on the properties of a neutral Higgs boson with mass about 125
GeV discovered at the LHC and present constraints obtained from precision
analysis of it. We also work out the properties of the extended Higgs sectors
which can be probed by present and future high-energy and high-precision
experiments. This review is intended to be as self-contained as possible aiming
at providing practical information for studying decays of Higgs bosons in the
SM and beyond.
