  Modern astrophysical and cosmological models are faced with two severe
theoretical difficulties, that can be summarized as the dark energy and the
dark matter problems. Relative to the former, it has been stated that cosmology
has entered a 'golden age', in which high-precision observational data have
confirmed with startling evidence that the Universe is undergoing a phase of
accelerated expansion. Several candidates, responsible for this expansion, have
been proposed in the literature, in particular, dark energy models and modified
gravity, amongst others. One is liable to ask: What is the so-called 'dark
energy' that is driving the acceleration of the universe? Is it a vacuum energy
or a dynamical field (''quintessence'')? Or is the acceleration due to
infra-red modifications of Einstein's theory of General Relativity? In the
context of dark matter, two observations, namely, the behavior of the galactic
rotation curves and the mass discrepancy in galactic clusters, suggest the
existence of a (non or weakly interacting) form of dark matter at galactic and
extra-galactic scales. It has also been proposed that modified gravity can
explain the galactic dynamics without the need of introducing dark matter. We
briefly review some of the modified theories of gravity that address these two
intriguing and exciting problems facing modern physics.
