After briefly summarizing the motivations for the A-CDM model, I will argue rather provocatively that the many candidates already reported by indirect detection experiments are a strong indication that it is nearly impossible to distinguish a WIMP annihilation signal from astrophysical background using the indirect detection method. This structural uncertainty argues strongly in favor of direct detection of WIMP interactions in the controlled environment of the laboratory and I will describe the main strategies developed to detect WIMPs using the direct detection technique in underground sites, protected from the cosmic-ray induced background. I will show that most of the present experimental efforts is now focused on three identification techniques of nuclear recoils, i.e. charge-phonon, light-phonon and charge-scintillation simultaneous detection. Finally, since direct detection has also its own candidate, I will comment on the DAMA annual modulation candidate, and on the lessons that can be learned from the long controversy over this result.