The Boltzmann picture is dominating the description of transport phenomena to such an extent that the kinetic framework is rarely questioned. Yet, whether kinetic variables are necessarily the ones to retain in the particle state vector is not a point over which to pass too quickly. For discrete particles in turbulent flows, there are typically three situations. The first one corresponds to fully-resolved turbulent flows, where the fluid velocity field is known at every point and every time, which means that the velocity of the fluid seen \({\mathbf {U}}_{\mathrm {s}}\) is similar to an external deterministic force field. It is then accounted for without approximation in Boltzmann-like PDF models based on the kinetic state vector \({\mathbf {Z}}_{\mathrm {p}}^{\mathrm {r}}=({\mathbf {X}}_{\mathrm {p}}, {\mathbf {U}}_{\mathrm {p}})\) where we handle the PDF \(p^{\mathrm {r}}(t;{\mathbf {z}}_{\mathrm {p}}^{\mathrm {r}})\) . The second situation corresponds to high-inertia particles for which the underlying fluid can be regarded as white-noise, leading to a Langevin equation for the discrete particle velocity and a resulting Fokker-Planck equation for \(p^{\mathrm {r}}\) . The third situation corresponds to the case of non-fully-resolved turbulent flows, where \({\mathbf {U}}_{\mathrm {s}}\) is neither deterministic nor white-noise but exhibits memory effects. Is the choice of kinetic variables still relevant in that case? And, if not, what guidelines can we follow? These are the questions addressed in this chapter.