Wand has made major, highly influential contributions to statistical methods for estimating mathematical functions. His field, variously known as nonparametric or flexible function estimation, or statistical smoothing, focuses on estimating functions under minimal structural assumptions. He has contributed substantially at all levels: to theory, methodology, software, education, and especially to applications. In terms of theory he has introduced techniques for exact risk analysis, made very influential contributions to multivariate local polynomial modelling, and developed methods for smoothing-parameter choice. His statistical software is widely used, and forms part of standard statistical packages. The many applications on which he has worked include the development of new, geoadditive technologies for epidemiology.