A short review paper is presented for the subject area of air quality modelling. The paper is geared towards equipping new researchers and workers with a basic appreciation for the technical aspects of their field, providing a staging point for further investigation, and highlighting useful source materials. The paper is introduced through a discussion of the philosophical and practical implications regarding mathematical air quality modelling. A critique of relevant mathematical modelling techniques is presented and includes a treatment of Box, Gaussian, Eulerian, Lagrangian and Particle modelling approaches. Conclusions on the future of mathematical air quality modelling are drawn.