We catalog 143 Ionian mountains (montes) and mountain-like features (mensae, tholi, plana, and small peaks) in order to investigate orogenic tectonism on Io. From this comprehensive list, we select 96 mountains for which there are sufficient coverage and resolution to discern spatial relationships with surrounding geologic features. Three of the 96 mountains are probably volcanoes, 92 appear to be tectonic massifs, and 1 is ambiguous. Of the 92 tectonic mountains, 38 abut paterae (volcanic or volcano-tectonic craters with irregular or scalloped margins). This juxtaposition is unlikely to be a coincidence as the probability of it occurring by chance is ~0.1%. We propose instead that orogenic faults may act as conduits for magma ascent, thus fueling patera formation near mountains. As resurfacing buries a shell of material from Io's surface to the base of the lithosphere, its effective radius is reduced and it heats up. We calculate the lithospheric volume change due to subsidence and thermal expansion as a function of lithospheric thickness. Conservation of volume dictates that this material must be uplifted at Io's surface. By estimating the total volume of the mountains, we are able to place a lower limit of 12 km on Io's lithospheric thickness. We hypothesize that, in some cases, mountain formation may be facilitated by asthenospheric diapirs impinging on the base of the lithosphere. The resulting lithospheric swell could focus the compressive stresses that drive orogenic tectonism. This model is one of several possible mechanisms for uplifting isolated mountains such as are observed on Io.