Herschel has opened new windows into studying the evolution of rapidly star-forming galaxies out to high redshifts. Today’s massive starbursts are characterized by star formation rates (SFRs) of  ~100 + M⊙ / yr and display a chaotic morphology and nucleated star formation indicative of a major merger. At z ~ 2, galaxies of similar mass and SFR are characterized by ordered rotation and distributed star formation. The emerging cold accretion paradigm provides an intuitive understanding for such differences. In it, halo accretion rates govern the supply of gas into star-forming regions, modulated by strong outflows. The high accretion rates at high-z drive more rapid star formation, while also making disks thicker and clumpier; the clumps are expected to be short-lived in the presence of strong galactic outflows as observed. Hence equivalently rapid star-formers at high redshift are not analogous to local merger-driven starbursts, but rather to local disks with highly enhanced accretion rates.