  Cosmological perturbations, originating in the quantum fluctuations of the
fields that drive inflation, are observed to be nearly scale invariant at the
largest scales. At smaller scales, however, perturbations are not severely
constrained and might be of particular importance if their amplitude is large.
They can trigger the creation of primordial black holes (PBHs) or stochastic
gravitational waves (GWs). Small-scale perturbations are generated during the
later stages of inflation, when possible strong features in the inflaton
potential can break scale invariance and leave characteristic imprints on the
spectrum. We focus on and review three types of features: inflection points and
steep steps in the potential, as well as sharp turns in the inflationary
trajectory in field space. We show that such features induce a strong
enhancement of the curvature spectrum within a certain wavenumber range. In
particular cases, they also generate characteristic oscillatory patterns that
are transferred in the spectrum of secondary GWs, which are potentially
observable by operating or designed experiments. We demonstrate these effects
through the calculation of the primordial power spectrum and the PBH abundance
in the context of $\alpha$-attractors and supergravity (SUGRA) models of
inflation.
