  We construct generalizations of the Kerr black holes by including higher
curvature corrections in the form of the Gauss-Bonnet density coupled to the
dilaton. We show that the domain of existence of these
Einstein-Gauss-Bonnet-dilaton (EBGd) black holes is bounded by the Kerr black
holes, the critical EGBd black holes, and the singular extremal EGBd solutions.
The angular momentum of the EGBd black holes can exceed the Kerr bound. The
EGBd black holes satisfy a generalised Smarr relation. We also compare their
innermost stable circular orbits with those of the Kerr black holes and show
the existence of differences which might be observable in astrophysical
systems.
