Abstract: Pressure anisotropies naturally arise in weakly collisional plasmas, and are ultimately limited by the pitch-angle scattering provided by various kinetic plasma instabilities. I will present particle-in-cell (PIC) plasma simulations of these instabilities, and will show that, in some regimes, their scattering can be highly inelastic and produce significant nonthermal particle acceleration. The presentation will focus on two astrophysical plasma environments: i) sub-relativistic, weakly collisional accretion disks around black holes (e.g., Sgr A*), where both electron and ion acceleration will be considered, and ii) non-relativistic, low beta plasmas relevant for solar flares, where the case of electron acceleration will be analyzed. I will review the main evidence for the existence of particle acceleration in these systems, and will discuss the importance that pressure anisotropy instabilities can have in helping explain these fascinating acceleration phenomena.