Observations provide increasingly strong evidence that the universe is accelerating. This revolutionary advance in cosmological observations confronts theoretical cosmology with a tremendous challenge, which it has so far failed to meet. Explanations of cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are nearly all based on a dark energy field with fine-tuned, unnatural properties. There is a great variety of models, but all share one feature in common -- an inability to account for the gravitational properties of the vacuum energy. Speculative ideas from string theory may hold some promise, but it is fair to say that no convincing model has yet been proposed. An alternative to dark energy is that gravity itself may behave differently from general relativity on the largest scales, in such a way as to produce acceleration. The alternative approach of modified gravity (or dark gravity) provides a new angle on the problem, but also faces serious difficulties, including in all known cases severe fine-tuning and the problem of explaining why the vacuum energy does not gravitate. The lack of an adequate theoretical framework for the late-time acceleration of the universe represents a deep crisis for theory -- but also an exciting challenge for theorists. It seems likely that an entirely new paradigm is required to resolve this crisis.

21 pages 10 figures Overview article for the dark energy issue of GRG revised to match version in print (minor typos corrected 4 refs. added)