Open any textbook on non-equilibrium statistical mechanics and you will find the Boltzmann equation as the archetypal description of particle-particle interactions. The Boltzmann equation is undoubtedly a major achievement and a well-established framework for short-range particle-particle interactions, especially for rarefied gases. It is therefore justified to refer to this framework when considering particle collisions in another context. The specific assumptions underlying the classical form of the Boltzmann equation are, however, often taken for granted. This can turn into a regrettable oversight since collisions of particles transported by random media challenge some aspects of the Boltzmann picture. With a view toward modeling particle collisions in turbulent flows, the purpose of this chapter is to revisit the key characteristics of the Boltzmann equation to bring out the limitations that need to be addressed.