  We use the Novikov-Thorne thin disk model to fit the thermal continuum X-ray
spectra of black hole X-ray binaries, and thereby extract the dimensionless
spin parameter a* = a/M of the black hole as a parameter of the fit. We
summarize the results obtained to date for six systems and describe work in
progress on additional systems. We also describe recent methodological
advances, our current efforts to make our analysis software fully available to
others, and our theoretical efforts to validate the Novikov-Thorne model.
