  In this Thesis by publication, we cover both phenomenological and theoretical
approaches to the study of inflation: from model-independent parametrizations
to modifications of gravity. In a review style, we provide a short introduction
to the standard cosmological model and an overview of the dynamics of the
canonical single-field inflationary scenario---including the dynamics and
evolution of the primordial quantum fluctuations and their signatures on
current observations. We then briefly discuss the Mukhanov parametrization, a
model-independent approach to study the allowed parameter space of the
canonical inflationary scenario. Later, we review the construction of the most
general scalar-tensor and scalar-vector-tensor theories of gravity yielding
second-order equations of motion, as well as the main models of inflation
developed within these frameworks. Finally, we demonstrate new techniques that
move beyond the slow-roll approximation---Generalized Slow-roll and Optimized
Slow-Roll---to compute the inflationary observables more accurately, in both
canonical and noncanonical scenarios. We complement the discussion with
detailed appendices on the cosmological perturbation theory and useful
expressions for the beyond-GR cosmology. Conclusions are drawn from the results
obtained for this Thesis.
