In this talk I will advocate for complementary strategies in Dark Matter (DM) searches. I will start by presenting some recent experimental results in the area of direct DM detection, where the SuperCDMS experiment has provided stringent upper bounds on the interaction strength of low-mass WIMPs. I will then show particle physics models that predict results in that range of masses, and that can also be motivated by the gamma-ray excess observed in the Fermi-LAT data from the Galactic Centre. I will then concentrate on how DM parameter can be reconstructed, and argue that only the combination of data from different sources would give unambiguous results with which the particle model for DM can be identified.