Many important contributions to the understanding of divertor physics are presented in this review of Alcator C-Mod research. The three regimes of parallel transport, sheath limited, conduction limited, and detached, were identified experimentally, along with their effects on plasma pressure along the magnetic field in the scrape-off layer. The extensive probe and bolometric coverage of the divertor allowed detailed characterization of the physics of detachment. The ability to dissipate ITER-like parallel power densities with extremely high divertor radiation emissivities (>40 MW/m3) was demonstrated under high-recycling and detached divertor conditions. The vertical plate divertor concept, developed and applied first on C-Mod, allowed the effect of divertor geometry to be studied, with the result that the vertical-plate and deep-slot geometries have a lower detachment threshold than the standard, flat-plate divertor. High-density (ne > 1 × 1021 m-3) divertor conditions allowed recombination to be more clearly observed in C-Mod than elsewhere. That, together with the development of spectroscopic techniques, enabled the only quantitative measurements of ion loss rate via recombination (and its role in detachment) as well as the trapping of hydrogenic Lyman alpha radiation. These were both shown to have important roles in detachment physics.