Informed by laboratory experiments and observations, models of volcanic eruptions have evolved from 1-D tools that explore parameterized processes into 2-D and 3-D calculations that explore combined or cascading interactions such as particle-fluid coupling, turbulent mixing, lightning generation, and aerosol production.  Greater computer speed has enabled these models to resolve dynamics related to source unsteadiness, heterogeneous turbulent mixing, jet compressibility, vent complexity, and complex thermochemical and thermophysical interactions among ash, gas, water and ice. These innovations have led to better understanding of processes, improved forecasting of real events, and assessing hazards ranging from pyroclastic flows, to ash clouds, to climate effects.  As models improve, so do observational data required for their validation.  New collection and analysis strategies are emerging. In this session we aim to bring together modelers, observers, and data scientists to explore eruption processes and how modeling helps forecast and assess hazards.