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 (ns > 1) or
by a large non-gaussianity parameter fNL, 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.