Mid-oceanic ridges and plumes are two major types of geodynamic features of the Earth and contribute significantly to terrestrial volcanism. Especially strong melt production in the mantle as well as increased crust formation and volcanic activity at the surface take place where a ridge and a plume coincide. This study combines a succinct survey of current knowledge on convection and melting in a plume--ridge setting with several series of numerical models probing the importance of various parameters for these processes; predictions of observables are also derived from the models. Emphasis is put on applications to Iceland, where such a setting is presently realized, and a geodynamic model for the upper mantle beneath Iceland is proposed.