Abstract: Chemical transport models (CTMs) are numerical simulations representing the interplay of emissions, chemistry, transport, microphysics, and deposition that determine the behavior of atmospheric aerosols.  As research tools, they play several important roles: assessing the significance of newly discovered or hypothesized processes in an atmospheric context, testing our knowledge of aerosol behavior against ambient observations, and predicting the impacts of policy decisions.  Conceptually, they are simple mass and population balances.  Complexity arises from several factors: the chemical and physical interactions of many dozen species; transport across a three-dimensional grid representing an urban airshed, a geographic region or even the entire globe; and the numerical approximations required to solve the resulting equations efficiently.  This tutorial will provide an overview of the essential components of CTMs, surveying the major algorithms for representing aerosol emissions, chemistry, microphysics, phase partitioning, transport, and deposition.  Special focus will be paid to numerical algorithms for representing aerosol size distributions and their evolution via the microphysical processes of condensation, coagulation, and nucleation.