I will review efforts by myself and my collaborators to investigate accretion flows onto black holes. We have developed fully-relativistic spectral models of accretion disks which can be compared directly with observations of Galactic X-ray binaries. I will discuss spectral fitting results for a number of sources which place constraints on the properties of both the accretion disks (e.g. the accretion stress) and the black holes (e.g. their spin). I will examine some of the assumptions which underly the models, and the related uncertainties in our constraints. In the process, I will briefly mention efforts to incorporate results from magnetohydrodynamics simulations into our models.
Received January 24, 2008