Approximately 85% of the mass of the universe is classified as dark matter, a type of matter outside the framework of the Standard Model. This thesis studies the phenomenology of three models that incorporate dark matter. Firstly, a singlet scalar dark matter candidate is added to two previously established models: the Higgslike dilaton and the Georgi-Machacek model. The parameters of these models are constrained using experimental results such as dark matter direct detection measurements, Higgs signal strengths, Higgs invisible width and the measured relic abundance of dark matter in the universe. The notion of self-interacting dark matter, derived from measurements of galaxy cluster Abell 3827, is also studied for SSDM extensions of both the Standard Model and the Two Higgs Doublet model. The parameters of these models are in each case tightly constrained by experiment.