Abstract: Understanding the dynamics of turbulent, weakly-collisional plasmas at kinetic scales is crucial to address long-standing issues, such as the dissipation of turbulent energy and the consequent plasma heating. Owing to the poor collisionality, kinetic-scale plasma turbulence naturally generates a large variety of non-equilibrium velocity-space structures in the plasma distribution function. This emerging complexity has been recently envisioned as a turbulent cascade occurring in the entire six-dimensional phase space. In this talk, I will review our latest results on this topic, obtained by exploiting both high-resolution Magnetospheric MultiScale (MMS) spacecraft measurements, and Eulerian Hybrid Vlasov-Maxwell numerical simulations. By Hermite-decomposing the proton velocity distribution function, I will show that the Hermite spectrum of the velocity distribution function displays a broadband, power-law behavior, whose slope is in agreement with theoretical expectations. The effect of the background magnetic field inducing a velocity-space spectral anisotropy, and the spatial intermittency of the velocity-space activity will be discussed as well. Finally, I will analyze the effect of inter-particle collisions that, despite being in general weak, inhibit the development of velocity-space cascade by dissipating fine velocity structures, thus restoring thermodynamic irreversibility.