While the dark matter has so far only revealed itself through the gravitational influence it exerts on its surroundings, there are good reasons to believe it is made up by WIMPs – a hypothetical class of heavy elementary particles not encompassed by the Standard Model of particle physics. The Inert Doublet Model constitutes a simple extension of the Standard Model Higgs sector. The model provides a new set of scalar particles, denoted inert scalars because of their lack of direct coupling to matter, of which the lightest is a WIMP dark matter candidate. Another popular Standard Model extension is that of supersymmetry. In the most minimal scenario the particle content is roughly doubled, and the lightest of the new supersymmetric particles, which typically is a neutralino, is a WIMP dark matter candidate. In this thesis the phenomenology of inert scalar and supersymmetric dark matter is studied. Relic density calculations are performed, and experimental signatures in indirect detection experiments and accelerator searches are derived. The Inert Doublet Model shows promising prospects for indirect detection of dark matter annihilations into monochromatic photons. It is also constrained by the old LEP II accelerator data. Some phenomenological differences between the Minimal Supersymmetric Standard Model and a slight extension, the Beyond the Minimal Supersymmetric Standard Model, can be found. Also, supersymmetric dark matter models can be detected already within the early LHC accelerator data.