This dissertation combines volcanological research of three convergent continental margins. Chapters 1 and 5 are general introductions and conclusions, respectively. Chapter 2 examines the spatiotemporal development of the Altiplano-Puna volcanic complex in the Lipez region of southwest Bolivia, a locus of a major Neogene ignimbrite flare- up, yet the least studied portion of the Altiplano-Puna volcanic complex of the Central Andes. New mapping and laser-fusion 40Ar/39Ar dating of sanidine and biotite from 56 locations, coupled with paleomagnetic data, refine the timing and volumes of ignimbrite emplacement in Bolivia and northern Chile to reveal that monotonous intermediate volcanism was prodigious and episodic throughout the complex. 40Ar/39Ar age determinations of 13 ignimbrites from northern Chile previously dated by the K-Ar method improve the overall temporal resolution of Altiplano-Puna volcanic complex development. Together with new and updated volume estimates, the new age determinations demonstrate a distinct onset of Altiplano-Puna volcanic complex ignimbrite volcanism with modest output rates beginning ~11 Ma, an episodic middle phase with the highest eruption rates between 8 and 3 Ma, followed by a general decline in volcanic output. The cyclic nature of individual caldera complexes and the spatiotemporal pattern of the volcanic field as a whole are consistent with both incremental construction of plutons as well as a composite Cordilleran batholith. Chapter 3 examines the spatiotemporal development of marine tephra deposits in deep sea sediment cores from the Sunda trench near Sumatra, which reveal evidence for seven large (minimum volume 0.6 - 6.3 km3), previously undocumented, explosive eruptions in this region over the last ~110,000 years, presumably sourced from mainland Sumatra. Sediment cores were collected within and adjacent to the Sunda trench from 3.3°N to 4.6°S at water depths between 1.8 and 5.5 km and distances of ~200 to 310 km from the active Sumatran volcanic arc. Glass shards within the tephra horizons were analyzed via the electron microprobe and laser ablation ICP-MS and define three compositional groups. Minimum volume estimates for the seven unique units are consistent with volcanic explosivity index (VEI; Newhall and Self, 1982) values of 4 - 5. The most frequent, widespread, and youngest deposits were found in the central region of the study area suggesting the central Sumatran arc as at the highest risk for large explosive eruptions. The first detailed chronological and geochemical data are presented for Tunupa volcano and nearby Huayrana lavas in chapter 4. New 40Ar/39Ar age determinations reveal edifice construction at ~1.5 Ma, a duration of ~90-240 k.y., and extrusion rates of 0.43 to 0.93 km3/k.y. Mineralogical compositional and textural data are consistent with shallow crustal storage (~7-18 km) and magma mixing. Volcano morphology, extrusion rates, mineralogy and textures are all similar to the Pleistocene to recent composite cones of the arc front, although new and available age data from the literature indicate that Western Cordilleran volcanism was concomitant with extrusion of both Huayrana (~11 Ma) and Tunupa (~1.5 Ma) lavas in the behind arc region. Arc-related volcanism was either widespread during these eruptive periods, or an additional melting mechanism was involved. Geochemical data, such as lower Ba/Nb ratios and enriched high field strength elemental concentrations, compared to volcanoes of the modern arc front suggest that Huayrana and Tunupa lavas were derived from a different source than the modern arc front. Geophysical and geochemical research in the central Andes indicate local variations in crustal and lithospheric thicknesses and compositions consistent with a dynamic continental lithosphere that has foundered in piecemeal fashion into the underlying asthenosphere throughout the mid to late Cenozoic. The data presented in this chapter for Tunupa and Huayrana indicate a complex petrogenetic origin and more research is necessary to determine the relative roles of arc and non-arc volcanism beneath the central Altiplano.