Near-surface reaction of CO₂-bearing fluids with silicate minerals in peridotite and basalt forms solid carbonate minerals. Such processes form abundant veins and travertine deposits, particularly in association with tectonically exposed mantle peridotite. This is important in the global carbon cycle, in weathering, and in understanding physical-chemical interaction during retrograde metamorphism. Enhancing the rate of such reactions is a proposed method for geologic CO₂ storage, and perhaps for direct capture of CO₂ from near-surface fluids. We review, synthesize, and extend inferences from a variety of sources. We include data from studies on natural peridotite carbonation processes, carbonation kinetics, feedback between permeability and volume change via reaction-driven cracking, and proposed methods for enhancing the rate of natural mineral carbonation via in situ processes (“at the outcrop”) rather than ex situ processes (“at the smokestack”).