After a brief introduction I will comment on some recently discussed approaches and WIMP candidates for dark matter, in particular on the supersymmetric neutralino with mass around 1 TeV which I currently favour. On the other hand, I will argue that, for a wide range of WIMPs, and independent of any specific particle physics scenarios, when a dark matter signal is eventually measured in direct or indirect search experiments, or both, it may prove rather challenging to work out ensuing WIMP properties.