We review the phenomenology of SUSY dark matter in various versions of MSSM, with universal and nonuniversal gaugino masses at the GUT scale. We start with the universal case (CMSSM), where the cosmologically compatible dark matter relic density is achieved only over some narrow regions of parameter space, involving some fine-tuning. Moreover, most of these regions are seriously challenged by the constraints from collider and direct dark matter detection experiments. Then we consider some simple and predictive nonuniversal gaugino mass models, based on SU(5) GUT. Several of these models offer viable SUSY dark matter candidates, which are compatible with the cosmic dark matter relic density and the above mentioned experimental constraints. They can be probed at the present and future collider and dark matter search experiments. Finally, we consider the nonuniversal gaugino mass model arising from anomaly mediated SUSY breaking. In this case the cosmologically compatible dark matter relic density requires dark matter mass of a few TeV, which puts it beyond the scope of collider and direct dark matter detection experiments. However, it has interesting predictions for some indirect dark matter detection experiments.