For a hundred years now, Einstein's General Relativity theory has played a pivotal role in our understanding of the Universe. But the recent realization of the accelerated cosmic expansion has put modern cosmology in crisis, mainly because this new realization implies most of the matter and energy content of the Universe exists in a not-yet-understood dark energy form. The existence of dark energy and dark matter (another little understood, non-luminous form of matter) has led to the conclusion that the general relativistic formulation of gravity does not provide a complete description of the Universe on large scales, and has therefore motivated the cosmology community in the search for new underlying physics. One possible modification of General Relativity comes in the form of f(R) theories of gravity. This book explores possible implications to cosmology of this class of modified gravitational physics.