This review provides a comprehensive overview of models of inflation and their predictions for primordial non-Gaussianity in density perturbations, which are believed to be the seeds for structures in the universe. Non-Gaussianity is a key observable that can discriminate between competing scenarios for the generation of cosmological perturbations and is a primary target of current and future Cosmic Microwave Background (CMB) satellite missions. The review covers both theoretical and observational aspects of non-Gaussianity, providing tools to compute the level of non-Gaussianity in any model of cosmological perturbations up to second order in perturbation theory. It discusses new models of inflation rooted in modern particle physics theory, which predict significant non-Gaussianity. The review also explores alternative mechanisms for generating cosmological perturbations, such as the curvaton and inhomogeneous reheating scenarios, and their implications for non-Gaussianity. Observational constraints on non-Gaussianity from CMB anisotropies are discussed, including the angular bispectrum and trispectrum, and the potential of future missions like Planck to detect non-Gaussian signals. The review concludes with a discussion of future prospects and the importance of non-Gaussianity in understanding the nature of the fundamental interactions.This review provides a comprehensive overview of models of inflation and their predictions for primordial non-Gaussianity in density perturbations, which are believed to be the seeds for structures in the universe. Non-Gaussianity is a key observable that can discriminate between competing scenarios for the generation of cosmological perturbations and is a primary target of current and future Cosmic Microwave Background (CMB) satellite missions. The review covers both theoretical and observational aspects of non-Gaussianity, providing tools to compute the level of non-Gaussianity in any model of cosmological perturbations up to second order in perturbation theory. It discusses new models of inflation rooted in modern particle physics theory, which predict significant non-Gaussianity. The review also explores alternative mechanisms for generating cosmological perturbations, such as the curvaton and inhomogeneous reheating scenarios, and their implications for non-Gaussianity. Observational constraints on non-Gaussianity from CMB anisotropies are discussed, including the angular bispectrum and trispectrum, and the potential of future missions like Planck to detect non-Gaussian signals. The review concludes with a discussion of future prospects and the importance of non-Gaussianity in understanding the nature of the fundamental interactions.