The quest for fundamental limitations on physical processes is old and venerable. Here, we investigate the maximum possible power, or luminosity, that any event can produce. We show, via full nonlinear simulations of Einstein's equations, that there exist initial conditions which give rise to arbitrarily large luminosities. However, the requirement that there is no past horizon in the spacetime seems to limit the luminosity to below the Planck value, L-P = c(5)/G. Numerical relativity simulations of critical collapse yield the largest luminosities observed to date, approximate to 0.2L(P). We also present an analytic solution to the Einstein equations which seems to give an unboundedly large luminosity; this will guide future numerical efforts to investigate super-Planckian luminosities.