  One of the most interesting and current phenomenological extensions of
General Relativity is the so-called $f (R)$ class of theories; a natural
generalization of this includes an explicit non-minimal coupling between matter
and curvature. The purpose of this work is to present a unified view of the
applicability 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 in the choice of Lagrangian
density, a mechanism to mimic galactic dark matter and a Cosmological Constant
at a astrophysical scale, the possibility of accounting for the accelerated
expansion of the Universe and modifications to post-inflationary reheating. The
equivalence between a model exhibiting a non-minimal coupling and
multi-scalar-theories is also discussed.
