This volume provides both an update and a review of the state of alternative theories of gravity, in connection with the issue of the accelerated expansion of the universe. Different theoretical proposals explain the acceleration in cosmic expansion, generating the dark energy issue and opening the possibilities of alternative theories of gravity (besides general relativity). Related issues, such as the problem of dark matter, are also surveyed in order to give the readers profound insight on the subject from different points of view. Comprised of short talks and plenary lectures given by leading experts in the field, some of them with brilliant and historic contributions, this book allows the reader to find referenced surveys in topics like f(R) theories, the dark matter and dark energy issues, Modified Newtonian Dynamics (MOND) scenarios, f(T) theories, scalar-tensor theories derived from non-Riemannian geometries, emergent universes, the cosmological constant and other topics of current interest for physicists and graduate students. These proceedings are from the Fourth International Meeting on Gravitation and Cosmology, held in Guadalajara, Jalisco, México, from 20 - 25 May, 2012, and were sponsored by ICTP- Trieste, Italy and COECyTJAL-Universidad de Guadalajara, México. This event is a series of scientific meetings that was started in 2004 in Cuba, focusing on current and selected topics in the fields of gravitation and cosmology.