A mechanism for the formation of polyelectrolyte multilayers is proposed. All of the experiments on such systems show that there is strong interpenetration of consecutive layers. We explain the very strong stability of the multilayers by the complexation between polyelectrolytes of opposite signs. Scaling laws on bulk polyelectrolyte complexation and their applications to the case of multilayers are derived in analogy with the description of neutral polymers under poor solvent conditions. Qualitative agreement is reached with some recent experiments.