  We discuss some fundamental issues underlying gravitational physics and point
out some of the main shortcomings of Einstein's General Relativity. In
particular, after taking into account the role of the two main objects of
relativistic theories of gravity, i.e. the metric and the connection fields, we
consider the possibility that they are not trivially related so that the
geodesic structure and the causal structure of the spacetime could be
disentangled, as supposed in the Palatini formulation of gravity. In this
perspective, the Equivalence Principle, in its weak and strong formulations,
can play a fundamental role in discriminating among competing theories. The
possibility of its violation at quantum level could open new perspectives in
gravitational physics and in unification with other interactions. We shortly
debate the possibility of equivalence principle measurements by ground-based
and space experiments.
