Ken-Ichi Nishikawa, Yosuke Mizuno, Jose L. Gomez, Ioana Duţan, Athina Meli, Jacek Niemiec, Oleh Kobzar, Martin Pohl, Hélène Sol, Nicholas MacDonald, Dieter H. Hartmann

• The particle-in-cell (PIC) method was developed to investigate microscopic phenomena, and with the advances in computing power, newly developed codes have been used for several fields, such as astrophysical, magnetospheric, and solar plasmas. PIC applications have grown extensively, with large computing powers available on supercomputers such as Pleiades and Blue Waters in the US. For astrophysical plasma research, PIC methods have been utilized for several topics, such as reconnection, pulsar dynamics, non-relativistic shocks, relativistic shocks, and relativistic jets. PIC simulations of relativistic jets have been reviewed with emphasis placed on the physics involved in the simulations. This review summarizes PIC simulations, starting with the Weibel instability in slab models of jets, and then focuses on global jet evolution in helical magnetic field geometry. In particular, we address kinetic Kelvin-Helmholtz instabilities and mushroom instabilities.