Modern cosmology has a well-based standard paradigm: the so-called ΛCDM model. This model assumes gravity to be described by General Relativity and cosmic acceleration, i.e. the fact that the universe is expanding in an accelerated way, is driven by the cosmological constant Λ while dark matter is considered to be cold. This model explains to an astonishing extend observations made of the cosmos on a large range of scales and times. Nevertheless, the increasing amount and precision of data gathered by cosmological surveys start giving tentative indications that parts of our standard model may require to be completed. Hence a significant amount of research in cosmology nowadays is conducted towards finding new proposals to perfect our description of the cosmos. A strong effort is made in this respect to search for more satisfactory descriptions of gravity and confront such proposals to observational data.