  Deviations from Gaussian statistics of the cosmological density fluctuations,
so-called primordial non-Gaussianities (NG), are one of the most informative
fingerprints of the origin of structures in the universe. Indeed, they can
probe physics at energy scales inaccessible to laboratory experiments, and are
sensitive to the interactions of the field(s) that generated the primordial
fluctuations, contrary to the Gaussian linear theory. As a result, they can
discriminate between inflationary models that are otherwise almost
indistinguishable. In this short review, we explain how to compute the
non-Gaussian properties in any inflationary scenario. We review the theoretical
predictions of several important classes of models. We then describe the ways
NG can be probed observationally, and we highlight the recent constraints from
the Planck mission, as well as their implications. We finally identify well
motivated theoretical targets for future experiments and discuss observational
prospects.
