This report reviews the development and applications of molecular and materials modeling in Europe and Japan in comparison to those in the United States. Topics covered include computational quantum chemistry, molecular simulations by molecular dynamics and Monte Carlo methods, mesoscale modeling of material domains, molecular-structure/macroscale property correlations like QSARs and QSPRs, and related information technologies like informatics and special-purpose molecular-modeling computers. The panel's findings include the following: The United States leads this field in many scientific areas. However, Canada has particular strengths in DFT methods and homogeneous catalysis; Europe in heterogeneous catalysis, mesoscale, and materials modeling; and Japan in materials modeling and special-purpose computing. Major government-industry initiatives are underway in Europe and Japan, notably in multi-scale materials modeling and in development of chemistry-capable ab-initio molecular dynamics codes. In European and U.S. assessments of nanotechnology, it was also concluded that to advance the field most quickly and competitively the need is acute for applying new and existing methods of molecularly based modeling. Additional findings are outlined in the panel's executive summary.