This study summarizes more than 15 years of scientific support for the United Nations-Economic Commission Europe (UN-ECE) Convention on Long Range Transboundary Air Pollution (LRTAP) and other European environmental protection conventions such as the Commission for the Protection of the Marine Environment of the North-East Atlantic (OSPAR) and the Baltic Marine Environment Protection Commission (HELCOM) by means of development and application of numerical simulation models for the atmospheric long-range transport of heavy metals. The work is mainly based on results and conclusions described in the nine papers of the appendix but some more recent investigations which have not yet been published in the scientific literature are also presented. An introductory overview and synthesis of current knowledge and understanding pertaining to all major aspects of heavy metals in the atmosphere is presented from a viewpoint that numerical modelling of their atmospheric processes is necessary and feasible to support the conventions mentioned above. The models discussed in this study have capabilities to quantify transboundary fluxes of lead, cadmium and mercury as the priority metals of concern and have a potential to identify sources as well as to predict the impact of emission reductions on the load of terrestrial and aquatic ecosystems in Europe. Advantages and limitations of relatively simple Lagrangian models are outlined within the context of issues currently facing the environmental scientific and policy making communities. However, a focus of this study is a comprehensive model system for atmospheric mercury species using a fully three-dimensional Eulerian reference frame and incorporating a state-of-science mercury chemistry scheme, which has been adopted by various scientific institutions for their modelling purposes.