The properties of the observed Higgs boson have been observed to be consistent with the SM predictions, however, the current data still leaves enough space for the Higgs to have non-standard decays. One such possibility is where the Higgs acts as a portal to BSM physics at the electroweak scale. An interesting prospect in this regard is to consider Higgs decaying into a pair of invisible particles in a BSM theory. In this seminar, I will first discuss the prospects of a 125 GeV Higgs boson decaying into light LSP neutralino dark matter (DM) in MSSM in the context of collider searches and astrophysical experiments. I will discuss the possibility to derive clues on the nature of the DM through complementarity between measurements at the future ILC and direct detection experiments. In the second part of my talk, I will discuss the current status and future prospects of a light neutralino DM in the phenomenologically richer NMSSM framework. I will discuss the relevant collider and astrophysical constraints and their effect on the NMSSM parameter space. I will present our results from the study of the projected reach of direct electroweakino searches at the future runs of LHC and their impact on the NMSSM parameter space. I will also talk about the future reach of DD and light Higgs searches on the currently allowed parameter space. Lastly, I will discuss the parameter space generated by a minimal extension of the SM by the local U(1) gauge group in order to accommodate a stable fermionic DM which also possesses adequate self-interaction. I will talk about the relevant constraints and their impact on the parameter space. I will also discuss the future collider reach of this simplified scenario.