  Particle acceleration in collisionless plasma systems is a central question
in astroplasma and astroparticle physics. The structure of the acceleration
regions, electron-ion energy equilibration, preacceleration of particles at
shocks to permit further energization by diffusive shock acceleration, require
knowledge of the distribution function of particles besides the structure and
dynamic of electromagnetic fields, and hence a kinetic description is
desirable. Particle-in-cell simulations offer an appropriate, if
computationally expensive method of essentially conducting numerical
experiments that explore kinetic phenomena in collisionless plasma. We review
recent results of PIC simulations of astrophysical plasma systems, particle
acceleration, and the instabilities that shape them.
