In materials with strong local Coulomb interactions, simple defects such as
atomic substitutions strongly affect both macroscopic and local properties of
the system. A nonmagnetic impurity, for instance, is seen to induce magnetism
nearby. Even without disorder, models of such correlated systems are generally
not soluble in 2 or 3 dimensions, and so few exact results are known for the
properties of such impurities. Nevertheless, some simple physical ideas have
emerged from experiments and approximate theories. Here, we first review what
we can learn about this problem from 1D antiferromagnetically correlated
systems. We then discuss experiments on the high Tc cuprate normal state which
probe the effect of impurities on local charge and spin degrees of freedom, and
compare with theories of single impurities in correlated hosts, as well as
phenomenological effective Kondo descriptions. Subsequently, we review theories
of impurities in d-wave superconductors including residual quasiparticle
interactions, and compare with experiments in the superconducting state. We
argue that existing data exhibit a remarkable similarity to impurity-induced
magnetism in the 1D case, implying the importance of electronic correlations
for the understanding of these phenomena, and suggesting that impurities may
provide excellent probes of the still poorly understood ground state of the
cuprates.Comment: 66 pages, 48 figures, review articl