The GeV and TeV emission from M82 and NGC 253 observed by Fermi, HESS, and VERITAS constrain the physics of cosmic rays (CRs) in these dense starbursts. We argue that the γ -rays are predominantly hadronic in origin, as expected by previous studies. The measured fluxes imply that pionic losses are efficient for CR protons in both galaxies: we show that a fraction F cal ≈ 0.2-0.4 of the energy injected in high-energy primary CR protons is lost to inelastic proton-proton collisions (pion production) before escape, producing γ -rays, neutrinos, and secondary electrons and positrons. We discuss the factor of ∼2 uncertainties in this estimate, including supernova rate and leptonic contributions to the GeV-TeV emission. We argue that γ -ray data on ULIRGs like Arp 220 can test whether M82 and NGC 253 are truly calorimetric, and we present upper limits on Arp 220 from the Fermi data. We show that the observed ratio of the GeV to GHz fluxes of the starbursts suggests that non-synchrotron cooling processes are important for cooling the CR electron/positron population. We briefly reconsider previous predictions in light of the γ -ray detections, including the starburst contribution to the γ -ray background and CR energy densities. Finally, as a guide for future studies, we list the brightest star-forming galaxies on the sky and present updated predictions for their γ -ray and neutrino fluxes.