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The seminal work by Bardeen, Cooper and Schrieffer taken further byEliashberg to the intermediate coupling solved the problem of conventionalsuperconductors about half a century ago. The Froehlich and Jahn-Tellerelectron-phonon interactions were identified as an essential piece of physicsin all novel superconductors. The BCS theory provides a qualitatively correctdescription of some of them like magnesium diborade and doped fullerenes (ifthe polaron formation is taken into account). However, cuprates remain aproblem. Here I show that the bipolaron extension of the BCS theory to thestrong-coupling regime could be a solution. Low-energy physics in this regimeis that of small 'superlight' bipolarons, which are real-space mobile bosonicpairs dressed by phonons. The symmetry and space modulations of the orderparameter are explained in the framework of the bipolaron theory. A d-waveBose-Einstein condensate of bipolarons reveals itself as a checkerboardmodulation of the hole density and of the gap below Tc.Comment: 5 pages, 1 figure, invited paper at the International Conference on  'Dynamic Inhomogenities in Complex Oxides' (June 2003, Bled, Slovenia

Superlight Bipolarons and a Checkerboard d-wave Condensate in Cuprates