  The actual accelerated expansion of the universe continues being a mystery in
physics. Some models had been proposed for this explanations, among them the
dark energy, which however has problems of experimental character as well as
theoretical. Other approximations, like modified gravity theories are an
interesting alternative for this problem. Motivated in this approach we study
cosmological models in f(R) theories which are natural extension of General
Relativity with arbitrary functions of the Ricci scalar. One chapter has
dedicated to obtain the modified field equations in the metric formalism of
f(R) theories, including the discussion about boundary terms in the action.
Later, we apply these equations in order to describe the dynamics of the
universe, using for this as space-time, the FLRW universe. We focus our study
in the problem of cosmological distances in f(R) theories. From the study of
the Geodesic Deviation Equation (GDE) in this modified scenario, we obtain
differential equations for the angular diameter distance, and as an extension,
the Dyer-Roeder like equation in f(R) gravity.
