We present a scaling theory to describe equilibrium conformations of weakly charged polyelectrolyte molecules grafted at one end onto impermeable surfaces of various morphologies (spheres, cylinders) and of arbitrary curvature. We focus on the case of sufficiently densely grafted chains, i.e., on curved polyelectrolyte blushes. Different regimes of the behavior of curved polyelectrolyte blushes can be distinguished, depending on grafting density, surface curvature, and chain length. We present phase diagrams of the system describing these regimes and discuss the crossover conditions. We also analyze the effect of charge annealing in curved polyelectrolyte brushes.