This article introduces general concepts and definitions related to the notion of asynchronous computation in the framework of artificial neural networks. Using the dynamic field theory as an illustrative example, we explain why one may want to perform such asynchronous computation and how one can implement it since this computational scheme draws several consequences on both the trajectories and the stability of the whole system. After giving an unequivocal definition of asynchronous computation, we present a few practically usable methods and quantitative bounds that can guarantee most of the mesoscopic properties of the system.