Peter Green is distinguished for his wide–ranging achievements in computational statistics. For example, his pioneering geometric algorithms have been important in the analysis of point patterns in spatial statistics. His work on semiparametric regression models has been seminal in bringing together the ideas of nonparametric regression and generalised linear models into a unified approach of wide applicability, illustrated by his own innovative applications of these and related novel approaches in fields as diverse as agricultural field experiments, reference curves for human growth and emission tomography. Most recently, his introduction and detailed development of reversible-jump Markov chain Monte Carlo computation has had an enormous impact in the burgeoning field of computational Bayesian statistics.