  This review covers the main aspects of black hole accretion disk theory. We
begin with the view that one of the main goals of the theory is to better
understand the nature of black holes themselves. In this light we discuss how
accretion disks might reveal some of the unique signatures of strong gravity:
the event horizon, the innermost stable circular orbit, and the ergosphere. We
then review, from a first-principles perspective, the physical processes at
play in accretion disks. This leads us to the four primary accretion disk
models that we review: Polish doughnuts (thick disks), Shakura-Sunyaev (thin)
disks, slim disks, and advection-dominated accretion flows (ADAFs). After
presenting the models we discuss issues of stability, oscillations, and jets.
Following our review of the analytic work, we take a parallel approach in
reviewing numerical studies of black hole accretion disks. We finish with a few
select applications that highlight particular astrophysical applications:
measurements of black hole mass and spin, black hole vs. neutron star accretion
disks, black hole accretion disk spectral states, and quasi-periodic
oscillations (QPOs).
