In this special issue of the European Journal of Applied Mathematics we celebrate the 75th birthday of its founding editor, Professor John Ockendon.

John started his research career with his D.Phil., awarded in 1965, working with Alan Tayler at the University of Oxford. John's background was in fluid mechanics, covering a wide range of topics, including, lubrication flows, flows in porous media, hypersonic aerodynamics, sloshing phenomena, and flow separation. He soon became involved in industrial research which led, in particular, to his interest in the field of free boundary problems, an area in which he became a driving force, through papers, conferences, and particularly through the fostering of regular international meetings and personal interactions. His pioneering work in the field was particularly concentrated in diffusion-controlled moving boundary problems that arise in various applications, such as in phase change problems, elastic-contact problems and the fundamental Hele-Shaw free boundary problem. The industrial collaborations also led to mathematical studies of lens design, fibre extrusion, fluidised beds, glass manufacture and semiconductor devices, to name but a few, and to problems in scattering and wave theory, non-linear wave propagation and non-linear oscillations, as well as mechanics and heat and mass transfer. He continues to work on PDEs and asymptotics applied to new well-founded models from the real world, with a particular focus in the physical and earth sciences.