  In this thesis, we investigate various possibilities of Weakly Interacting
Massive Particle (WIMP) dark matter (DM) and their implications. These
possibilities are important because they challenge the viability of WIMP DM in
light of tight constraints from experiments such as direct detection. We begin
by analyzing a fermion dark matter possibility with an axion-like particle
(ALP) portal. We consider theoretical and experimental limits related to
neutrino and ALP data within a certain mass range, and we find the allowed
parameter space. This possibility resolves the problem of the lack of direct
detection of WIMP DM through the ALP portal. Furthermore, we examine the limits
on photon signals from HESS and Fermi-LAT data. Next, we look at a
two-component scalar and fermion dark matter possibility, following a similar
approach to our previous work. This simple possibility requires only a few
additional fields and symmetries to explain neutrino mass and dark matter
candidates. By finding parameter space that satisfies various bounds, such as
relic density, direct detection, and invisible Higgs width, we show that both
scalar and fermion particles can serve as DM. This possibility is consistent
and offers a rich spectrum of phenomenology that can be tested through
collider-based experiments. In our final work, we removie the extra Z2 symmetry
and added a new pseudoscalar particle in our two compoent model. We test this
pseudoscalar particle against multiple DM and non-DM related bounds, including
DM lifetime bound, Planck bound, direct-detection limits from various target
materials, and invisible Higgs width. The possibility exhibits a significant
parameter space for our pseudoscalar DM while being in agreement with
theoretical and experimental limits.
