  We review the noncommutative spectral geometry, a gravitational model that
combines noncommutative geometry with the spectral action principle, in an
attempt to unify General Relativity and the Standard Model of electroweak and
strong interactions. Despite the phenomenological successes of the model, the
discrepancy between the predicted Higgs mass and the current experimental data
indicate that one may have to go beyond the simple model considered at first.
We review the current status of the phenomenological consequences and their
implications. Since this model lives by construction at high energy scales,
namely at the Grand Unified Theories scale, it provides a natural framework to
investigate early universe cosmology. We briefly review some of its
cosmological consequences.
