Einstein’s 1905 seminal paper, wherefrom the rather skeptical quotation opening this chapter is taken from, is the gateway to the physics of Brownian motion, the archetype of the subject of this chapter: random (often called stochastic) processes, a designation that indicates processes where randomness plays a leading role. By “process” we usually mean a series of events taking place in an ordered sequence, so the most common case (but not necessarily the only one) is that of processes happening in time. The crux of the matter is that we can distinguish what precedes (in time or space) an event from what follows it. This already suggests that random time processes are intrinsically linked with the arrow of time and, consequently, with irreversibility. Indeed, we will see that the link between Brownian motion and diffusion discovered by Einstein necessarily leads to relate random fluctuations to dissipation effects.