  A new concept of nonlinear focusing of colliding bunches, called Crab Waist
(CW)collision scheme, has been proposed at LNF INFN. It has been successfully
tested at the Italian lepton collider DAFNE in operational conditions providing
luminosity for two different experimental detectors, SIDDHARTA and KLOE-2.
Considering a high efficiency of the scheme for increasing collision luminosity
and its relative simplicity for implementation several new collider projects
have been proposed and are under development at present. These are the
SuperKEKB B-factory ready to start commissioning in 2016 in Japan, the
SuperC-Tau factory proposed in Novosibirsk and entered in the short list of
Russian mega-science projects, the new 100-km electron-positron Future Circular
Collider (FCC-ee) under design study at CERN and some others. In this paper we
describe the CW collision scheme, discuss its advantages and report principal
results achieved at the electron-positron Phi-factory DAFNE.
