Numerical simulations have shown that the recently proposed crab waist scheme of beam-beam collisions can substantially boost the luminosity of existing and future electron-positron colliders. In this paper we describe the crab waist concept and discuss potential advantages that such a scheme can provide. We also present the results of beam-beam simulations for the two currently proposed projects based on the crab waist scheme: the DAFNE upgrade and the Super B-factory project.