f(R) Theories

Over the past decade, <i>f</i>(<i>R</i>) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of <i>f</i>(<i>R</i>) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.