The properties of a polyelectrolyte brush depend on a broad range of parameters including the characteristics of the polyions, salt concentration, ion valence, and solvent conditions. We present a non-mean-field theory for polyelectrolyte brushes and discuss the effects of salt concentration, polymer grafting density, and chain length on the polyion configurations, the electrostatic potential, and the distributions of both counterions and coions. Comparison will be attempted with pertinent experimental results and with established theoretical predictions. Special attention will be given to systems containing multivalent counterions wherein the electrostatic interactions are coupled with the excluded-volume effects that defy typical mean-field calculations and scaling analysis. We found that multivalent counterions result in a non-monotonic swelling of the brush that is qualitatively different from that for the case of monovalent counterions. In the limit of low salt concentration, trivalent counterions may self-organize into a one-dimensional wave-like structure in between tethered polyions and lead to a first-order phase transition similar to that for a neutral brush in a poor solvent.