What is the dark energy paradigm?

The present accelerated expansion of the universe is a major challenge for cosmology. Dark Energy models aim to explain this unconventional expansion. We have at the present time a large variety of models which are conceptually very different. We review here some of them, especially those based on a modification of the laws of gravity. Future high precision observations probing both the background and the perturbations will significantly reduce the class of viable models. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim