  The seminal work by Bardeen, Cooper and Schrieffer taken further by
Eliashberg to the intermediate coupling solved the problem of conventional
superconductors about half a century ago. The Froehlich and Jahn-Teller
electron-phonon interactions were identified as an essential piece of physics
in all novel superconductors. The BCS theory provides a qualitatively correct
description of some of them like magnesium diborade and doped fullerenes (if
the polaron formation is taken into account). However, cuprates remain a
problem. Here I show that the bipolaron extension of the BCS theory to the
strong-coupling regime could be a solution. Low-energy physics in this regime
is that of small 'superlight' bipolarons, which are real-space mobile bosonic
pairs dressed by phonons. The symmetry and space modulations of the order
parameter are explained in the framework of the bipolaron theory. A d-wave
Bose-Einstein condensate of bipolarons reveals itself as a checkerboard
modulation of the hole density and of the gap below Tc.
