  A review on numerical simulations of galaxy formation is given. Different
numerical methods to solve collisionless and gas dynamical systems are outlined
and one particular simulation technique, Smoothed Particle Hydrodynamics, is
discussed in some detail. After a short discussion of the most relevant
physical processes which affect the dynamics of the gas, the success and
shortcomings of state of the art simulations are discussed via the example of
the formation of disk galaxies.
