Classical and quantum systems: transport due to rare events

We review possible mechanisms for energy transfer based on 'rare' or 'non-perturbative' effects, in physical systems that present a many-body localized phenomenology. The main focus is on classical systems, with or without quenched disorder. For non-quantum systems, the breakdown of localization is usually not regarded as an issue, and we thus aim at identifying the fastest channels for transport. Next, we contemplate the possibility of applying the same mechanisms in quantum systems, including disorder free systems (e.g. Bose-Hubbard chain), disordered many-body localized systems with mobility edges at energies below the edge, and strongly disordered lattice systems in $d>1$. For quantum mechanical systems, the relevance of these considerations for transport is currently a matter of debate.