What makes the Universe accelerate? A review on what dark energy could be and how to test it

Explaining the origin of the acceleration of the expansion of the Universe remains as challenging as ever. In this review, we present different approaches from dark energy to modified gravity. We also emphasize the quantum nature of the problem and the need for an explanation which should violate Weinberg's no go theorem. This might involve a self-tuning mechanism or the acausal sequestering of the vacuum energy. Laboratory tests of the coupling to matter of nearly massless scalar fields, which could be one of the features required to explain the cosmic acceleration, are also reviewed.