Stochastic processes enter Quantum Mechanics from different corners: from a measurement perspective since, upon monitoring, quantum systems evolve randomly due to information readout and random back-action, and from a statistical physics perspective, since the evolution of open quantum systems acquires some randomness through their interaction with external environmentsor reservoirs. We shall discuss aspects of both facets and present illustrative examples dealing, in one hand, with the emergence of quantum spikes — which are stochastic partners dressing quantum jumps — under strong monitoring, and in the other hand, with the characterisation of steady fluctuations in noisy extended systems.