A short overview on Higgs physics at the LHC and LHeC

The Higgs boson is the cornerstone of the Standard Model (SM) of Particle Physics. The Large Hadron Collider (LHC) experiments observed a particle with a mass interval of 125-127 GeV and somewhat compatible with the Higgs boson of the SM. However, the SM has to be extended, to resolve major theoretical shortcomings such as Hierarchy problem, in a "Supersymmetric ways". The simplest extensions, e.g., Minimal Supersymmetric SM (MSSM) and Next-to-MSSM(NMSSM), leads to presence of multiple Higgs bosons. Even without Supersymmetry, the SM could well be extended simply by adding one or more Higgs doublets -- one such is Type-III 2-Higgs Doublet Model(2HDM-III). The most striking features of this model is that one can look for the favor--violating signatures of the Higgs bosons. We shall give a short overview on Higgs boson phenomenology at the LHC and upcoming Large Hadron electron Collider(LHeC) experiments in the above mentioned models in a very pedagogical ways.