In this chapter, we explore the use of stochastic processes as models for physical phenomena, with a particular focus on their application to turbulence. Our aim is to offer a concise overview of key stochastic tools and their use from a physicist’s perspective, while also directing the reader to further references for more detailed and mathematically rigorous developments. We begin with the historically significant phenomenon of Brownian motion-often referred to in physics as the starting point for modern stochastic process theory. From there, we briefly introduce the central concepts behind multiscale analysis in physical systems. This approach often leads to replacing complex deterministic descriptions with simpler, effective stochastic models-a powerful and widely used method at the core of modern statistical mechanics. Within the context of microscopic physics, we discuss how model complexity can be reduced depending on the time scale of observation. As a practical example of this methodology, we provide an introductory overview of stochastic modelling in turbulence-a field that has seen widespread application. Before that, we offer a brief review of the phenomenological theory of turbulence to provide necessary background. We conclude by presenting some recent research results that lie at the intersection of statistical mechanics and dynamical systems theory. This work centres around a conjecture proposed by Giovanni Gallavotti. The conjecture enables the identification of globally smooth solutions for a set of equations equivalent to the Navier–Stokes equations-something that has not yet been achieved directly. It also frames turbulence within the broader context of non-equilibrium statistical mechanics. The structure of this chapter follows, in large part, a series of lectures delivered at the Prague school, though we have highlighted only the most essential aspects. This overview is not intended to be exhaustive or fully comprehensive but is meant to serve as an entry point for readers interested in further exploration of the topics discussed.