Monaghan is internationally distinguished for his development of smoothed particle hydrodynamics (SPH). This computational technique is ideal for handling gravitating gas-dynamical systems, and has had an enormous influence on contemporary computational astrophysics, particularly in the vast cosmological simulations that illuminate the evolution of the universe. The technique has many applications outside astrophysics, and Monaghan’s own work is distinguished by its breadth of application to astrophysical, geophysical and engineering problems. Monaghan’s SPH technique is so important that there is a series of annual international meetings specifically on the subject of SPH and its applications.