Radiative feedback (RFB) from stars plays a key role in galaxies, but remains poorly understood. We explore this using high-resolution, multifrequency radiation-hydrodynamics (RHD) simulations from the Feedback In Realistic Environments (FIRE) project. We study ultrafaint dwarf through Milky Way mass scales, including H+He photoionization; photoelectric, Lyman Werner, Compton, and dust heating; and single+multiple scattering radiation pressure (RP). We compare distinct numerical algorithms: ray-based LEBRON (exact when optically thin) and moments-based M1 (exact when optically thick). The most important RFB channels on galaxy scales are photoionization heating and single-scattering RP: in all galaxies, most ionizing/far-UV luminosity (∼1/2 of lifetime-integrated bolometric) is absorbed. In dwarfs, the most important effect is photoionization heating from the UV background suppressing accretion. In MW-mass galaxies, metagalactic backgrounds have negligible effects; but local photoionization and single-scattering RP contribute to regulating the galactic star formation efficiency and lowering central densities. Without some RFB (or other 'rapid' FB), resolved GMCs convert too-efficiently into stars, making galaxies dominated by hyperdense, bound star clusters. This makes star formation more violent and 'bursty' when SNe explode in these hyperclustered objects: thus, including RFB 'smoothes' SFHs. These conclusions are robust to RHD methods, but M1 produces somewhat stronger effects. Like in previous FIRE simulations, IR multiple-scattering is rare (negligible in dwarfs, ∼ 10 per cent of RP in massive galaxies): absorption occurs primarily in 'normal' GMCs with AV ∼ 1.