The goal of the Chemistry-Climate Model Validation (CCMVal) activity is to improve understanding of chemistry-climate models (CCMs) through process-oriented evaluation and to provide reliable projections of stratospheric ozone and its impact on climate. An appreciation of the details of model formulations is essential for understanding how models respond to the changing external forcings of greenhouse gases and ozone-depleting substances, and hence for understanding the ozone and climate forecasts produced by the models participating in this activity. Here we introduce and review the models used for the second round (CCMVal-2) of this intercomparison, regarding the implementation of chemical, transport, radiative, and dynamical processes in these models. In particular, we review the advantages and problems associated with approaches used to model processes of relevance to stratospheric dynamics and chemistry. Furthermore, we state the definitions of the reference simulations performed, and describe the forcing data used in these simulations. We identify some developments in chemistry-climate modeling that make models more physically based or more comprehensive, including the introduction of an interactive ocean, online photolysis, troposphere-stratosphere chemistry, and non-orographic gravity-wave deposition as linked to tropospheric convection. The relatively new developments indicate that stratospheric CCM modeling is becoming more consistent with our physically based understanding of the atmosphere.