There are several broad classes of mathematical models used to apportion the aerosol measured at a receptor site to its likely sources. This paper surveys the two types applied in exercises for the Mathematical and Empirical Receptor Models Workshop (Quail Roost II): chemical mass balance models and multivariate models. The fundamental principles of each are reviewed. Also considered are the specific models available within each class. These include: tracer element, linear programming, ordinary linear least-squares, effective variance least-squares and ridge regression (all solutions to the chemical mass balance equation), and factor analysis, target transformation factor analysis, multiple linear regression and extended Q-mode factor analysis (all multivariate models). In practical application of chemical mass balance models, a frequent problem is the presence of two or more emission sources whose signatures are very similar. Several techniques to reduce the effects of such multicollinearity are discussed. The propagation of errors for source contribution estimates, another practical concern, also is given special attention.