  One of the major themes in correlated electron physics over the last quarter
century has been the problem of high-temperature superconductivity in
hole-doped copper-oxide compounds. Fundamental to this problem is the
competition between antiferromagnetic spin correlations, a symptom of strong
Coulomb interactions, and the kinetic energy of the doped carriers, which
favors delocalization. After discussing some of the early challenges in the
field, I describe the experimental picture provided by a variety of
spectroscopic and transport techniques. Then I turn to the technique of neutron
scattering, and discuss how it is used to determine spin correlations,
especially in model systems of quantum magnetism. Neutron scattering and
complementary techniques have determined the extent to which antiferromagnetic
spin correlations survive in the cuprate superconductors. One experimental case
involves the ordering of spin and charge stripes. I first consider related
measurements on model compounds, such as La(2-x)Sr(x)NiO(4+d), and then discuss
the case of La(2-x)Ba(x)CuO(4). In the latter system, recent transport studies
have demonstrated that quasi-two-dimensional superconductivity coexists with
the stripe order, but with frustrated phase order between the layers. This has
led to new concepts for the coexistence of spin order and superconductivity.
While the relevance of stripe correlations to high-temperature
superconductivity remains a subject of controversy, there is no question that
stripes are an intriguing example of electron matter that results from strong
correlations.
