A comprehensive understanding of the origin, nature, and significance of volcanic unrest is currently missing, but of fundamental imp0l1ance to communities living with the threat of volcanic hazards. My thesis addresses this shortcoming from a volcanic deformation angle. By incorporating a range of multi-disciplinary data, I have developed new integrated models of volcanic deformation using Finite Element Analysis (FEA) that are suitable for use in both forward and inverse modelling approaches. They are consistent with independent geophysical observables and provide detailed insight on volcanic processes during unrest crises. I have applied these models to three volcanoes. A study of Uturuncu volcano, Bolivia, highlighted the importance of subsurface structure and time-dependent source processes in explaining both the spatial and temporal deformation patterns. The combined results alluded to a diapiric-type ascent of magma. At Cotopaxi volcano, Ecuador, I used novel inversion models employing FEA to elucidate the location and volume of a magmatic intrusion during an aseismic, and non-eruptive, unrest episode. The models also provided insights into observable signals that could be associated with future intrusive or eruptive activity. My analysis of the persistent inflation at Aira caldera, Japan, during an ongoing emptive phase at Sakurajima volcano, used inverse Finite Element models to, for the first time, quantify the statistical significance of including topography and subsurface heterogeneity in deformation models. Additional models results were used to identify the rate, timing, volume, location and mechanism of magma supply, as well as the timescales that could be associated with increases in future eruptive activity. Together, these results highlight how models with more plausible, and geophysically consistent, components can improve our understanding of the mechanical processes affecting volcanic unrest and geodetic eruption precursors. They provide a framework to help advance emption forecasting and risk mitigation.