We study the role of massive perturbers (MPs) in deflecting stars and binaries to almost radial (``loss-cone'') orbits, where they pass near the central massive black hole (MBH), interact with it at periapse q, and are ultimately destroyed. MPs dominate dynamical relaxation when the ratio of the 2nd moments of the MP and star mass distributions, mu _2\!\equiv\!<=ft.N_p<=ft< ngle M_p2\right\rangle \right/N_\star<=ft< ngle M_\star2\right\rangle , satisfies mu _2\!\gg\!1. The observed MPs in the nucleus of the Galaxy (giant molecular clouds and stellar clusters), and plausibly in late type galaxies generally, have 102\!<=sssim\! mu _2\!<=sssim\!105. MPs thus shorten the relaxation timescale by 102-5 relative to 2-body relaxation by stars alone. We show this increases by 101-3 the rate of large-q interactions with the MBH, where loss-cone refilling by stellar 2-body relaxation is inefficient. We extend the Fokker-Planck loss-cone formalism to approximately account for relaxation by rare encounters with MPs. We show that binary-MBH exchanges driven by MPs may explain the origin of the young main sequence B stars that are observed very near the Galactic MBH, and may increase by orders of magnitude the ejection rate of hyper-velocity stars. We suggest that MP-driven relaxation plays an important role in the capture of stars on very tight orbits around the MBH, leading to their tidal orbital decay and disruption or to inspiral through the emission of gravitational waves from zero-eccentricity orbits. We show that loss-cone refilling by MPs leads to rapid orbital decay and coalescence of binary MBHs, thereby solving the stalling problem.