Subsequent to a brief review of the mathematical tools that are required, the concept of the simulation pipeline, "from model derivation to the simulation", is applied to 14 example scenarios from diverse fields such as "Game theory - deciding - planning", "Traffic on highways and data highways", "Dynamical systems" and "Physics in the computer". Whether it is game theory or mathematical finance, traffic or control theory, population dynamics or chaos, or molecular dynamics, continuum mechanics or computer graphics - the reader gains insight into the world of simulation in a descriptive yet systematic way.