Cosmological inflation is one of the leading paradigm in modern cosmology, It does not only provides a dynamical explanation for the homogeneity and isotropy of the universe on large scales, but it also predicts the generation of primordial cosmological perturbations, originating from quantum fluctuations of fields, which generate the observed inhomogeneities e.g. in the cosmic microwave background (CMB). Although these perturbations are usually assumed to be very small, there are very important phenomenological consequences if we allow them to grow during inflation, such as the generation of Primordial Black Holes (PBHs), a candidate for Dark Matter. In this talk I will explore and compare two mathematical setups that allow us to study these rare large inhomogeneities during inflation in a non-linear way: the deltaN formalism and the stochastic approach to inflation.