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ECMI is the brand associated with European mathematics for industry and organizes successful biannual conferences. In this series, the 16th conference was held in the Historical City Hall of Wuppertal (Germany). It covered mathematics in a wide range of applications and methods, from Circuit and Electromagnetic Device Simulation, Model Order Reduction for Chip Design, Uncertainties and Stochastics, Production, Fluids, Life and Environmental Sciences to Dedicated and Versatile Methods. §These proceedings of ECMI 2010 emphasize mathematics as an innovation enabler for industry and business, and as an absolutely essential pre-requiste for Europe on its way to becoming the leading knowledge-based economy in the world.