The atmosphere overlying the ocean is very sensitive - physically, chemically and climatically - to air pollution. Given that clouds over the ocean are of great climatic significance, and that sulphate aerosols seem to be an important control on marine cloud formation, anthropogenic inputs of sulphate to the marine atmosphere could exert an important influence on climate. Recently, sulphur emissions from fossil fuel burning by international shipping have been geographically characterized, indicating that ship sulphur emissions nearly equal the natural sulphur flux from ocean to atmosphere in many areas. Here we use a global chemical transport model to show that these ship emissions can be a dominant contributor to atmospheric sulphur dioxide concentrations over much of the world's oceans and in several coastal regions. The ship emissions also contribute significantly to atmospheric non-seasalt sulphate concentrations over Northern Hemisphere ocean regions and parts of the Southern Pacific Ocean, and indirect radiative forcing due to ship-emitted particulate matter (sulphate plus organic material) is estimated to contribute a substantial fraction to the anthropogenic perturbation of the Earth's radiation budget. The quantification of emissions from international shipping forces a re- evaluation of our present understanding of sulphur cycling and radiative forcing over the ocean.