  We examine an extension of General Relativity with an explicit non-minimal
coupling between matter and curvature. The purpose of this work is to present
an overview of the implications of the latter to various contexts, ranging from
astrophysical matter distributions to a cosmological setting. Various results
are discussed, including the impact of this non-minimal coupling on the choice
of Lagrangian density, on a mechanism to mimic galactic and cluster dark
matter, on the possibility of accounting for the accelerated expansion of the
Universe, energy density fluctuations and modifications to post-inflationary
reheating. The equivalence between a model exhibiting a non-minimal coupling
and multi-scalar-theories is also discussed.

General Relativity and Quantum Cosmology