  Cosmological inflation is the dominating paradigm to account for observations
of the Cosmic Microwave Background (CMB). In this thesis, we study the
phenomenology of a class of particularly well motivated models of inflation,
known under the generic name of hybrid models. They are characterised by a
transition from a valley to a hilltop shaped potential. In particular, we study
three limiting regimes of the simplest realisation, hybrid inflation,
constraining its parameter space using observational bounds on the spectral
index and the non-gaussianity of the primordial perturbations. We find that the
model is highly constrained by observations, with large part of the parameter
space either ruled out by a blue spectral index ($n_s>1$) or by a large
non-gaussianity parameter $f_{rm NL}$, two quantities measured with precision
by PLANCK. However, there exists regions in parameter space leading to
interesting phenomenology compatibly with observational bounds. Also, a version
of hybrid inflation with a third light scalar field at horizon crossing is
derived from the supersymmetry framework. We find that the model can generate
observables within observational bounds.
