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We review three different kinds of experiments that emphasize the non-BCS, inhomogeneous aspects of superconductivity in the high Tc cuprates. The first is the existence of two different energy scales in the superconducting state, initially identified by a comparison between tunneling and Andreev–Saint–James spectroscopies [Deutscher, Nature (London) 397, 410 (1999)]. The second are EXAFS measurements of the Cu-O bond length distribution, which have shown that below a temperature T* > Tc, it becomes broader than expected from the Debye-Waller broadening and presents a split [Bianconi etal, Phys. Rev. Lett. 76, 3412 (1996)]. The third one is the effect of frozen lattice disorder on critical current and vortex pinning, which profoundly affects the pairing landscape [Gutierrez etal, Nature Mater. 6, 367 (2007)]. We then discuss how these results fit with models in which the electron-lattice interaction plays a leading role.