How fast do interactions occur between individuals is central in ecology. Functional responses are classically used to describe the number of predation, mating, competition, etc. in a given timeframe. Hundreds of different forms of functional responses have been proposed in the ecological and mathematical literature. It is well known that this form can dramatically affect the stability and dynamics of populations. Yet, the forms given to functional responses are generally poorly justified from the individual point of view, most ecologists generally adopting a phenomenological approach, in a purely deterministic framework. Here, we propose a novel and original stochastic approach based on the renewal theory. We show how it is possible to derive classical and novel functional responses from the behaviors of the individuals by modelling the time taken by all activities that must be fulfilled for an interaction to be successful. We show how a stochastic approximation of the functional responses can be obtained thanks to the renewal theory. We give applications of our theoretical framework and discuss the importance of interactions as a source of stochasticity in ecological models.