Pumping and stirring effects in quantum physics have counterparts in purely classical stochastic and dissipative processes. The studies of quantum pumping and of quantum stirring emphasize the role of quantum interference in the analysis of the induced current. A major objective is to calculate the amount Q of transported particles per a driving cycle. There are circumstances in which Q is an integer number due to the topology of parameter space. More generally Q is affected by inter-particle interactions, disorder, chaos, noise and dissipation.