Many of the most important scientific problems can be modeled mathematically by a combination of reaction and transport equations. Giving just a few examples, consider chemical reactors, combustion, the growth of microorganism in bioreactors, ocean ecology models on larger scales, atmospheric dynamics, or nuclear reactions in fusion reactors or suns. Both fields, reaction kinetics and transport equations, have had have their distinctive developments, often leading to mathematical incompatibilities between the two theories. In my talk I will discuss and propose numerical schemes that are based on the idea of transported reaction volumes, based mainly on particle methods discretising the transport models. This makes it possible to avoid the dual continuum limit for both the transport equation and the reaction kinetics. We like a construction that, for example, makes it possible to consider the reaction scheme as a stochastic process, and the transport deterministic. Important in such numerical approaches will be the idea of overlapping reaction volumes, i.e. we must consider the possibility that reacting particles in neighbouring reaction volumes are allowed to react with each other.