The Eocene to Recent histories of the central parts of the oceanic Aleutian and continental Andean arcs are distinctive in being non extensional, having accretionary and non-accretionary stages and in being punctuated by episodes of foreland migration of the arc front linked to forearc subduction erosion. The Central Aleutian arc began at ~ 50 Ma with a rapid magmatic buildup of the ridge. The crust reached a thickness of ~35 km by 35 Ma in response to magmatic addition, likely aided by contraction. Xenoliths provide evidence for a wehrlitic to gabbroic cumulate/granulitic crust at depth before 35 Ma. The 35 -31 Ma calc-alkaline Hidden Bay pluton intruded as this cycle waned with sporadic evidence for residual garnet best explained by melting of granulite/eclogite facies crust from the forearc in the mantle wedge as the trench advanced northward. A renewed plutonic cycle was present to the north at ~ 14 Ma with a less voluminous arc front yet further north at 7-5 Ma. The latest major overall northward shift of the arc occurred between 13 and 3 Ma. The arc became accretionary in the Pliocene as glacial sediments, whose trace element signals appear in the arc magmas, accumulated in the trench. In contrast, the Eocene to Recent history of the Central Andes records a transition from an accretionary to a non-accretionary margin with pre-mid Miocene magmas displaying subducted sediment signatures that diminish by the late Miocene as the sediment supply decreases to the east. Major foreland shifts in the volcanic arc in the Eocene and the late Miocene correlate with peaks in residual garnet signatures suggesting recycling of forearc crust in the mantle wedge along with crustal thickening and delamination in the backarc. A 600 km long eastward shift of the magmatic arc at ~7-3 Ma could correlate with removal of up to 50 km of the forearc as major changes occurred across the backarc. Driving forces are associated with changing subduction geometry and varying degrees of trenchward advance of the overriding plate. Forearc subduction erosion provides a mechanism to explain the preservation of upper crustal accessory mineral in mantle derived ophiolite suites.