The sample paths of most stochastic processes are rather oscillatory. One of the interesting consequences of this property is that additive functionals of such processes enjoy a lot of cancellation/averaging. This regularisation phenomenon of the noise has been long of interest in connection to local times, skew processes, quadrature problems, fluid dynamics, or stochastic quantisation. We overview some old and new approaches in stochastic and pathwise analysis to study these regularising effects.