The limits of volcanology are currently being expanded through quantitative approaches, employed to investigate volcanoes, understand their dynamics, and forecast their hazards. Increasing resources of computing power, new analytical methods and experimental facilities are advancing and deepening our understanding of magmatic processes. Direct observations by various geophysical and geochemical instruments are providing important constraints of subsurface magma movements and eruption processes. This also applies to the increasingly detailed sampling of deposits and improved quantitative methods of processing field data. This session invites contributions on quantitative and innovative approaches to open questions and problems in volcanology, especially by young scientists who will take over the duty of addressing new advances and defining new directions, and are therefore especially encouraged to contribute. We welcome contributions applying theoretical, numerical, and experimental approaches, studies on volcanic hazards, as well as direct observations of volcanic processes and their deposits. There is also increased recognition by the community that multi-disciplinary approaches combining several methods is needed to advance our knowledge of processes and effectively address the hazards posed by volcanoes. The session is co-sponsored by the Marie Curie Initial Training Network NEMOH (www.nemoh-itn.eu).