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A phenomenological model of a system of antiferromagnetically correlated spins is shown to give a good quantitative description of NMR, nuclear-quadrupole-resonance, and Knight-shift measurements on yttrium, planar copper, and planar oxygen sites in YBa2Cu307. The antiferromagnetic correlation length is estimated to be -2.5 lattice constants at T =100 K. The temperature dependence of the correlation length ceases at T"=100K. The enhancement of the observed relaxation rates over what is expected for weakly interacting electrons is calculated and shown to be large. Extension of the calculation to other cuprate superconductors is discussed.Fermi liquid, the spin-lattice relaxation rate, 8' has the Korringa temperature dependence O'-T. This temperature dependence may be understood as follows: for a Fermi liquid the density of states for spin cxcitations is constant at low energies. The rate is given by the number of thermally excited spin excitations, which in this case scales as T. In the high-T, cuprate superconductors, the Cu relaxation rate 8' varies more slowly than the Korringa rate for T& T*. The crossover temperature T* 42

Although nineteen years have passed since the discovery of high temperature cuprate superconductivity [1], there is still no consensus on its physical origin. This is in large part because of a lack of understanding of the state of matter out of which the superconductivity arises. In optimally and underdoped materials, this state exhibits a pseudogap at temperatures large compared to the superconducting transition temperature [2,3]. Although discovered only three years after the pioneering work of Bednorz and Müller, the physical origin of this pseudogap behavior and whether it constitutes a distinct phase of matter is still shrouded in mystery. In the summer of 2004, a band of physicists gathered for five weeks at the Aspen Center for Physics to discuss the pseudogap. In this perspective, we would like to summarize some of the results presented there and discuss the importance of the pseudogap phase in the context of strongly correlated electron systems.

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The idea of superconductivity without the mediating role of lattice vibrations (phonons) has a long history. It was realized soon after the publication of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity 50 years ago that a full treatment of both the charge and spin degrees of freedom of the electron predicts the existence of attractive components of the effective interaction between electrons even in the absence of lattice vibrations--a particular example is the effective interaction that depends on the relative spins of the electrons. Such attraction without phonons can lead to electronic pairing and to unconventional forms of superconductivity that can be much more sensitive than traditional (BCS) superconductivity to the precise details of the crystal structure and to the electronic and magnetic properties of a material.