Chemical transport models (CTMs) are important tools used to explore pollution transport pathways and to assess the impact of long-range transport on air pollutant concentrations in specific regions. There is growing interest in estimating the contribution of emission sources both near and far on ambient pollution levels. However, quantification requires methods for the diagnosis and analysis of intercontinental transport and dispersion, as well as procedures to track the contributions of specific source regions to pollution levels over regions of interest (i.e. the source-receptor (S/R) relationships). Such analyses are being done with regional and global scale CTMs. In this chapter we discuss the various modelling methods and approaches being used to predict pollution levels over regional and global scales, with a focus on issues related to estimating S/R relationships. Previously published estimates of the hemispheric transport of O3, aerosols and subsequent deposition of various aerosol components are presented, as well as preliminary results from the model intercomparison organized under the Task Force, hereinafter referred to as the HTAP intercomparison. In addition, the capabilities and limitations of current models are analysed, 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.