Cosmology is in a golden age, and some experiments of high complexity are running up or have been proposed in order to know about the properties of our Universe and test theoretical cosmological models. So, it is pertinent to study some of these models and confront them with observations. In this book we use the ?N formalism to study the statistical descriptors for some cosmological inflationary models that allow us to obtain large levels of non-gaussianity and violations of the statistical isotropy. Basically, we study two different classes of models: a class of models that includes only scalar field perturbations, specifically a subclass of small-field slow-roll models of inflation with canonical kinetic terms, and the class of models that admits both vector and scalar field perturbations. The theoretical results are compared with the most recent observations and the available parameter window where these models are valid is extracted. This book will be of great help for both graduate students and researchers interested in the latest developments in the subjects of primordial non-gaussianity and statistical anisotropy.