Mixture models play a central role in statistical science, and Professor Geoffrey McLachlan’s pioneering work in this field has been especially influential. His research on mixture models for inference and clustering is of particular note, as is his work on applications of the EM algorithm, especially to complex multivariate problems. Geoffrey has also made major contributions to error-rate estimation for classifiers and to new techniques in analysing gene expression data, including techniques for clustering tissue samples containing thousands of genes, and for controlling false discovery rate.