Effective implementation of policy to decrease ambient pollutant levels requires knowledge of the contribution of pollutant sources (e.g., from natural sources versus those due to human activities, or from local versus regional versus intercontinental sources) to the observed pollutant distributions. While observational methods provide clear evidence for intercontinental transport, and can help fingerprint specific source contributions (see Chapter 2), these measurements are generally not in operational networks, and are often not regionally representative. Thus at present, observation-based approaches alone cannot provide the information on source attribution (S/A) and source/receptor (S/R) relationships needed to make better informed policy decisions about hemispheric pollution. Numerical models incorporate our current understanding of the physical and chemical processes which control atmospheric composition, and are designed to predict the relationships between emissions and the resulting pollution distributions in the atmosphere. These models allow us to explore the importance of different processes and to attribute observed enhancements in pollutant concentrations to particular sources. In this chapter we discuss methods for quantifying intercontinental transport using numerical models, and summarize recent estimates of the magnitude and uncertainty in these effects, both from the published literature and from the model intercomparison organized under the Task Force (hereafter referred to as the HTAP intercomparison). The capabilities and limitations of current models are analyzed, along with the sensitivity of S/R relationships to future changes in emissions and climate. Further activities needed to improve the modelling capabilities and the estimates of hemispheric transport of pollutants are identified.