Independent observations of normal-state pseudogaps in a number of magnetic and kinetic measurements (chapter 6) and unusual critical phenomena (chapter 7) tell us that many cuprates may not be BCS superconductors. Indeed their superconducting state is as anomalous as the normal one. In particular, there is strong evidence for a d-like order parameter (changing sign when the CuO2 plane is rotated by π/2) in cuprates [251]. A number of phase-sensitive experiments [252] provide unambiguous evidence in this direction; furthermore, the low-temperature magnetic penetration depth [253, 254] was found to be linear in a few cuprates as expected for a d-wave BCS superconductor. However, superconductor–insulator–normal metal (SIN) and superconductor–insulator–superconductor (SIS) tunnelling studies (sections 8.2 and 8.3), the c-axis Josephson tunnelling [255] and some high-precision magnetic measurements [256] show a more usual s-like symmetry or even reveal an upturn in the temperature dependence of the penetration depth below some characteristic temperature [257]. Also both angle-resolved photoemission spectroscopy (ARPES) [264] and scanning tunnelling microscopy (STM) [265] have shown that the maximum energy gap is many times larger and the 2Δ/T C ratio is well above that expected in weak-coupling BCS theory (~3.5) or in its intermediate-coupling generalization (chapter 3).