Spectral densities connect correlation functions computed in quantum field theory to observables measured in experiments. For strongly-interacting theories, their non-perturbative determinations from lattice simulations are therefore of primary importance. They entail the inverse Laplace transform of correlation functions calculated in Euclidean time. In this talk I will describe a recent proposal for their definition and extraction based on the Mellin transform, both in the continuum and on the lattice, with their corresponding generalization to smeared spectral densities, together with possible outlooks.