The 1995-present eruption of Soufrière Hills Volcano on Montserrat has produced over a cubic kilometre of andesitic magma, creating a series of lava domes that were successively destroyed, with much of their mass deposited in the sea. There have been five phases of lava extrusion to form these lava domes: November 1995-March 1998; November 1999-July 2003; August 2005-April 2007; July 2008-January 2009; and October 2009-February 2010. It has been one of the most intensively studied volcanoes in the world during this time, and there are long instrumental and observational datasets. From these have sprung major new insights concerning: the cyclicity of magma transport; low-frequency earthquakes associated with conduit magma flow; the dynamics of lateral blasts and Vulcanian explosions; the role that basalt-andesite magma mingling in the mid-crust has in powering the eruption; identification using seismic tomography of the uppermost magma reservoir at a depth of 5.5 >7.5 km; and many others. Parallel to the research effort, there has been a consistent programme of quantitative risk assessment since 1997 that has both pioneered new methods and provided a solid evidential source for the civil authority to use in mitigating the risks to the people of Montserrat.