%0 Journal Article %T f(R) Theories %A Antonio De Felice %A Shinji Tsujikawa %J Living Reviews in Relativity %D 2010 %I Max-Planck Institute for Gravitational Physics %X Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity ¨C 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¨CDicke theory and Gauss¨CBonnet gravity, and address models that can satisfy both cosmological and local gravity constraints. %K inflation %K dark energy %K cosmological perturbations %K f(R) gravity %K modified gravity %U http://www.livingreviews.org/lrr-2010-3