After having examined the deterministic motility of swimming cells, we now turn to their interactions with a fluctuating environment. We consider in this thirteenth chapter the motion of small microorganisms subject to thermal noise, a situation relevant to the locomotion of small bacteria. This allows us to introduce two modelling approaches, namely a discrete framework (along with ensemble averaging) and a continuum probabilistic framework, both of which we adapt for the modelling of collective dynamics in the next chapter. We first review Brownian motion in translation and rotation for a passive particle, introduce all the relevant timescales for its dynamics, show how the statistical properties of its trajectory can be captured with both discrete and continuum frameworks, and apply these concepts to the diffusion of cells. By adding a swimming velocity to the particle, we next show how thermal noise affects the motion of swimming microorganisms and in turn how the noisy run-and-tumble motion of bacteria can be described as an effective diffusive process.