Magmas erupted in deep-water environments (> 500 m) are subject to physical constraints that are very different to those for subaerial eruptions, including hydrostatic pressure, bulk modulus, thermal conductivity, heat capacity and the density of water mass, which are generally orders of magnitude greater than for air. The exsolved volatile content of the erupting magma will generally be lower because magmas decompress to hydrostatic pressures orders of magnitude greater than atmospheric pressure. At water depths and pressures greater than those equivalent to the critical points of H2O and CO2, exsolved volatiles are supercritical fluids, not gas, and so have limited ability to expand, let alone explode. Gas overpressures are lower in deep submarine magmas relative to their subaerial counterparts, limiting the degree of explosive fragmentation. Explosive intensity is further minimised because of the higher bulk modulus of water, relative to air. Higher retention of volatiles makes subaqueously erupted magmas less viscous, and more prone to fire fountaining eruption style compared with compositionally equivalent subaerial counterparts. The high heat capacity and thermal conductivity of (ambient) water makes the effusively (and/or explosively) erupted magmas more prone to rapid cooling and quench fragmentation, producing non-explosive hyaloclastite breccia. Subaqueous eruption columns or plumes form above both explosive and non-explosive eruptions, consisting of heated water, supercritical fluid and gas, and both can entrain pyroclasts and pumice autoclasts upwards. The height of such plumes is limited by the water depth and will show different buoyancy, dynamics, and height and dispersal capacity compared with subaerial eruption columns. Water ingress, condensation and dissolution erosion of gas bubbles will be major factors in controlling column dynamics. Autoclasts and pyroclasts with an initial bulk density less than water can rise buoyantly, irrespective of plume buoyancy. Dispersal and sedimentation of clasts in water is affected by the rate at which buoyant clasts become water-logged and sink, and by wind, waves, and oceanic currents, which can produce very circuitous dispersal patterns in floating pumice rafts. Floating pumice can abrade by frictional interaction with neighbours in a floating raft, and generate in transit, post-eruptive ash fallout unrelated to explosive activity or quench fragmentation.