  This thesis is devoted to the study of gravitational theories which can be
seen as modifications or generalisations of General Relativity. The motivation
for considering such theories, stemming from Cosmology, High Energy Physics and
Astrophysics is thoroughly discussed (cosmological problems, dark energy and
dark matter problems, the lack of success so far in obtaining a successful
formulation for Quantum Gravity). The basic principles which a gravitational
theory should follow, and their geometrical interpretation, are analysed in a
broad perspective which highlights the basic assumptions of General Relativity
and suggests possible modifications which might be made. A number of such
possible modifications are presented, focusing on certain specific classes of
theories: scalar-tensor theories, metric f(R) theories, Palatini f(R) theories,
metric-affine f(R) theories and Gauss--Bonnet theories. The characteristics of
these theories are fully explored and attention is payed to issues of dynamical
equivalence between them. Also, cosmological phenomenology within the realm of
each of the theories is discussed and it is shown that they can potentially
address the well-known cosmological problems. A number of viability criteria
are presented: cosmological observations, Solar System tests, stability
criteria, existence of exact solutions for common vacuum or matter
configurations etc. Finally, future perspectives in the field of modified
gravity are discussed and the possibility for going beyond a trial-and-error
approach to modified gravity is explored.
