This report includes a general and mathematical description of advection, dispersion, sorption and other processes important for contaminant transport in polluted soils. The significance of the diverse processes depends on the pollutant and the physical and chemical conditions of the specific site. An overview is given of the ground location of different types of substances together with processes with large influence on transport. When selecting a computer based transport model it is essential to know which processes have the largest impact. The reason is that different processes can be described mathematically in varying ways at the same times as different numerical methods are suitable involving different mathematical problems. Often it is crucial whether advection or dispersion dominates the contaminant transport. Concurrently it is stated that the main problem in computer based modelling often is the quality of input data and not the numerical methods. In saturated zone, below the groundwater level, there are several methods at hand for managing three-dimensional problems. However, the processes in the unsaturated zone are more difficult to describe and today one- and two-dimensional models are most common. Examples are given on different models and software packages currently used for modelling contaminant transport.