Quantum fluctuations play an essential role in the dynamics and phenomenology of inflation in the very early universe. Usually quantum fluctuations during inflation are studied perturbatively (often linearly) about a fixed classical background, but in the stochastic approach quantum fluctuations on small scales provide a stochastic contribution to the non-perturbative classical evolution on large (super-Hubble) scales. In particular the stochastic delta-N formalism can be used to study large density perturbations required to form primordial black holes. This relies on the separate universe viewpoint but does not necessarily require slow roll (though the system is particularly simple in slow roll). I will discuss some of the issues when applying the stochastic approach beyond slow-roll.