  We discuss constraints on supersymmetric models arising from the relic
density measurements of WMAP as well as from direct and precision measurements,
LEP, b-sgamma, g-2, Bs-mumu. We consider mSUGRA models and their extensions
with non-universal gaugino masses. We find, as commonly known, that the relic
density pinpoints towards very specific regions of the mSUGRA models:
coannihilation, focus and Heavy Higgs annihilation. The allowed regions widen
significantly when varying the top quark mass. Introducing some
non-universality in the gaugino masses significantly changes this conclusion as
in specific non-universal models the relic density upper limit can be easily
satisfied. This occurs with models where M1>M2 at the GUT scale when the LSP
has a high wino component. Models where M3<M2 favours the Higgs annihilation
channel in large regions of parameter space and at large $\tan\beta$ also
favours the annihilation of neutralinos in gauge bosons pairs.We discuss also
the potential of direct detection experiments to probe supersymmetric models
and point out at the main consequences for colliders based on the mass
spectrum. Our calculation of the relic density of neutralinos is based on
micrOMEGAs and the SUSY spectrum is generated with SoftSUSY
