During three close flybys in late 1999 and early 2000 the Galileo spacecraft acquired new observations of the mountains that tower above Io's surface. These images have revealed surprising variety in the mountains' morphologies. They range from jagged peaks several kilometers high to lower, rounded structures. Some are very smooth, others are covered by numerous parallel ridges. Many mountains have margins that are collapsing outward in large landslides or series of slump blocks, but a few have steep, scalloped scarps. From these observations we can gain insight into the structure and material properties of Io's crust as well as into the erosional processes acting on Io. We have also investigated formation mechanisms proposed for these structures using finite-element analysis. Mountain formation might be initiated by global compression due to the high rate of global subsidence associated with Io's high resurfacing rate; however, our models demonstrate that this hypothesis lacks a mechanism for isolating the mountains. The large fraction (∼40%) of mountains that are associated with paterae suggests that in some cases these features are tectonically related. Therefore we have also simulated the stresses induced in Io's crust by a combination of a thermal upwelling in the mantle with global lithospheric compression and have shown that this can focus compressional stresses. If this mechanism is responsible for some of Io's mountains, it could also explain the common association of mountains with paterae.