At least since the middle Miocene (∼16 Ma), subduction erosion has been the dominant process controlling the tectonic evolution of the Pacific margin of Costa Rica. Ocean Drilling Program Site 1042 recovered 16.5 Ma nearshore sediment at ∼3.9 km depth, ∼7 km landward of the trench axis. The overlying Miocene to Quaternary sediment contains benthic foraminifera documenting margin subsidence from upper bathyal (∼200 m) to abyssal (∼2000 m) depth. The rate of subsidence was low during the early to middle Miocene but increased sharply in the late Miocene‐early Pliocene (5–6.5 Ma) and at the Pliocene‐Pleistocene boundary (2.4 Ma). Foraminifera data, bedding dip, and the geometry of slope sediment indicate that tilting of the forearc occurred coincident with the onset of rapid late Miocene subsidence. Seismic images show that normal faulting is widespread across the continental slope; however, extension by faulting only accounts for a minor amount of the post‐6.5 Ma subsidence. Basal tectonic erosion is invoked to explain the subsidence. The short‐term rate of removal of rock from the forearc is about 107–123 km3 Myr−1 km−1. Mass removal is a nonsteady state process affecting the chemical balance of the arc: the ocean sediment input, with the short‐term erosion rate, is a factor of 10 smaller than the eroded mass input. The low 10Be concentration in the volcanic arc of Costa Rica could be explained by dilution with eroded material. The late Miocene onset of rapid subsidence is coeval with the arrival of the Cocos Ridge at the subduction zone. The underthrusting of thick and thermally younger ocean crust decreased the subduction angle of the slab along a large segment of the margin and changed the dynamic equilibrium of the margin taper. This process may have induced the increase in the rate of subduction erosion and thus the recycling of crustal material to the mantle.