  We investigate the capability of directional detectors to probe neutralino
dark matter in the Minimal Supersymmetric Standard Model and the
Next-to-Minimal Supersymmetric Standard Model with parameters defined at the
weak scale. We show that directional detectors such as the future MIMAC
detector will probe spin dependent dark matter scattering on nucleons that are
beyond the reach of current spin independent detectors. The complementarity
between indirect searches, in particular using gamma rays from dwarf spheroidal
galaxies, spin dependent and spin independent direct search techniques is
emphasized. We comment on the impact of the negative results on squark searches
at the LHC. Finally, we investigate how the fundamental parameters of the
models can be constrained in the event of a dark matter signal.
