The problems of transportation and traffic are as old as man's history of transportation. The type of vehicles changed over the centuries and so did traffic problems and the ways one tried to solve them. The evolution of traffic in this century can be characterized by a vast increase in the number of cars. This process was followed by an expanding network of roads and streets trying to keep up with the increasing demand. At the same time new methods to control the traffic were advanced. They include simple and intelligent traffic lights as well as sufficient information and rerouting services.
Essential for the development of such a controlling mechanism is a detailed understanding of the traffic flow. A large number of models have been applied. Most of them are concerned with the one-dimensional vehicle flow on a road without intersections. In this paper, three different approaches will be described: a fluid dynamics model, a model based on the dynamics of individual vehicles and cellular automata (CA). All three predict traffic jams when a critical density is reached but the properties of the congested phases are rather different. The traffic flow in cities requires two-dimensional models. Three different approaches based on CA will be discussed.