Abstract : The embedding of cosmological inflation in high-energy physics motivates the construction of scenarios involving several scalar fields or/and non-standard actions. These scenarios generate primordial fluctuations whose deviations from Gaussianity can now be probed with an interesting accuracy and we study in this thesis the corresponding observational signatures. We first expose the relativistic theory of cosmological perturbations and the mechanism by which they are created during inflation. We then present a review of the different types of models that generate large primordial non-Gaussianities as well as of the methods to determine the latter. We present in particular several applications from a formalism known as covariant. We then deal with an inflationary scenario inspired by string theory known as Dirac-Born-Infeld inflation, and notably its multifield aspects. We finally describe the means carried out to detect the effects of primordial non-Gaussianities on the cosmological observables.