The protection of the environment is one of the most important problems facing us today. Reliable and robust strategies for keeping pollution caused by harmful chemicals under safe levels have to be developed and used routinely. Large mathematical models, incorporating all important physical and chemical processes, can solve this task, but the computational burden is huge. The papers presented here describe some of the difficult problems that have to be solved during the development of large scale air pollution models, and different ways to solve them. The work involves combined research by specialists in the fields of environmental modelling, numerical analysis and scientific computing. Further, if models are to run in real time (which may be vital in the case of accidental hazardous releases), then new and efficient methods that harness the potential power of parallel supercomputers must be developed, so that actual computing speed starts to approach the maximum available performance. The articles are understandable by specialists in the field of air pollution modelling, as well as specialists in the many other related areas.