  In many plasmas, in particular in space science, protons govern much of the
essential physics. Minority ions, suprathermal tails, and electrons at times
account for additional details. However, electron effects usually appear on
much smaller spatial and temporal scales. For more than two decades, scientists
have refined computational models that concentrate on the dominating and
larger-scale ion kinetic physics, while treating the much lighter electrons as
a charge-neutralizing fluid. These physics-based, algorithmic model
descriptions are called hybrid codes, which have established an invaluable
position for themselves - clearly distinct from MHD calculations, but simpler
and much more efficient than full-particle simulations. Here, the foundation
and numerical details of hybrid codes are reviewed, and differences between
existing algorithms are elucidated.
