  We have developed a new numerical code to study the evolution of distorted,
rotating black holes. We discuss the numerical methods and gauge conditions we
developed to evolve such spacetimes. The code has been put through a series of
tests, and we report on (a) results of comparisons with codes designed to
evolve non-rotating holes, (b) evolution of Kerr spacetimes for which analytic
properties are known, and (c) the evolution of distorted rotating holes. The
code accurately reproduces results of the previous NCSA non-rotating code and
passes convergence tests. New features of the evolution of rotating black holes
not seen in non-rotating holes are identified. With this code we can evolve
rotating black holes up to about $t=100M$, depending on the resolution and
angular momentum. We also describe a new family of black hole initial data sets
which represent rotating holes with a wide range of distortion parameters, and
distorted non-rotating black holes with odd-parity radiation. Finally, we study
the limiting slices for a maximally sliced rotating black hole and find good
agreement with theoretical predictions.
