f(R) gravity: successes and challenges

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We review the state of the art of f(R) theories of gravity (in their various formulations), which have been proposed as an explanation of the cosmic acceleration alternative to dark energy. The successes of f(R) gravity are discussed, together with the challenges imposed by minimal criteria for their viability.
18 pages, latex. Presented at SIGRAV2008, 18th Congress of the Italian Society of General Relativity and Gravitation, Cosenza, Italy September 22-25, 2008

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