These notes review recent efforts to model turbulent small scales by noise and derive the consequences of such a simplified description. The simplest case is the action of a turbulent fluid on a passive scalar. Far from being completely understood—think of the Rayleigh-Benard problem—this is at least the case where the results are more numerous and obtained by different approaches. For a comparison, we think it is very interesting to have a self-contained description of the deterministic approach, namely the theory of diffusion approximation by homogenisation. Thus is the first section of the notes, after the introduction. Then, we present a relatively recent stochastic approach to the same problem, based on a stochastic model of the turbulent small scales, and see its power. This is the second section. Then we move to the effect of turbulent small scales of a fluid on the large scales of the fluid itself. First, in the third section, we describe the Lagrangian approach to the scale decomposition. The classical Eulerian decomposition is more rational but does not allow one to reach the same clean results. We try to justify the Lagrangian decomposition by several arguments, including a reference subsection to the vortex-wave system. Finally, in the fourth section, we show that the stochastic equations for the large scales, perturbed by small scales in transport form, allow us to extend the diffusion limit arguments of the second section to a nonlinear framework.