In this work I aim to point out some theoretical issues and caveats in DM search. In the first chapters I review the evidence for DM existence, the DM candidates and the different kinds of DM experimental search. The bulk of the work investigates three different topics. In the first topic, concerning neutrino from the Sun, I show the fact that evaporation does not allow to probe part of the parameter space, in the low mass range. In the second one, I show that, like in the case of the detected positron excess, that could be explained both by DM or by astrophysical source, even a possible excess of antiprotons could suffer from the same kind of degeneracy. In the third part, I consider DM search at collider. I point out some problems about using the EFT low-energy approximation at LHC, arising from the fact that the experimental bounds and the average energy of collisions at LHC are of the same order of magnitude. Afterward, to take this fact into account, I propose a method to rescale experimental bounds, and I review an alternative way of analyzing experimental results, that is using Simplified Models. Finally, I also show which is the part of the parameter space for both Simplified Models and EFT giving the DM the right relic abundance, in the case of thermal freeze-out
