"With four parameters I can fit an elephant,          
and with five I can make him wiggle his trunk."
With this "aphorism", John von Neumann, one of the most brilliant mathematicians and co-founder of computational physics, may have pointed out the main reason for the gigantic success numerical modelling has experienced during the last decades. Having huge amounts of processing capabilities at our disposal, almost anything between simulation of nano-scaled molecular chains up to cosmological disribution and collapse of hydrogen clouds forming galaxies seems possible. Yet the hint of cynicism in his statement, should always remind us of being aware of how model assumptions, algorithms, and their implementations affect our results.

The intention of this lecture is to give a short review on the great achievments, common methods as well as traps one will encounter in the vast field of numerical astronomy.