  Much excitement surrounds the possibility that strontium ruthenate exhibits
chiral p-wave superconducting order. Such order would be a solid state analogue
of the A phase of He-3, with the potential for exotic physics relevant to
quantum computing. We take a critical look at the evidence for such
time-reversal symmetry breaking order. The possible superconducting order
parameter symmetries and the evidence for and against chiral p-wave order are
reviewed, with an emphasis on the most recent theoretical predictions and
experimental observations. In particular, attempts to reconcile experimental
observations and theoretical predictions for the spontaneous supercurrents
expected at sample edges and domain walls of a chiral p-wave superconductor and
for the polar Kerr effect, a key signature of broken time-reversal symmetry,
are discussed.
