Once upon a time, the problem started with a question: can the addition of (some kind of) noise improve structural properties of infinite-dimensional systems, such as existence, uniqueness, regularity, stability, etc.? First, we will discuss some finite-dimensional examples in which the answer is positive, as well as some infinite dimensional examples, to convince our readers that this question is worth asking. We will then tell about some of the early attempts, made by a few groups, to obtain additional properties of solutions (mainly Markovianity, relaxation to equilibrium) by means of the underlying probabilistic structure.