Stable Oscillations of Black Hole Accretion Discs

The study of stable accretion disc oscillations relevant to black hole candidate (BHC) systems dates back over twenty years. Prior work has focused on both unstable and (potentially) stable disc oscillations. The former has often been suspected of being the underlying cause for the observed broad-band variability in BHC, whereas the latter has had little observational motivation until quite recently. In this article, we review both the observations and theory of (predominantly) stable oscillations in BHC systems. We discuss how variability, both broad-band and quasi-periodic, is characterized in BHC. We review previous claims of low frequency features in BHC, and we discuss the recent observational evidence for stable, high frequency oscillations in so-called `galactic microquasars'. As a potential explanation for the latter observations, we concentrate on a class of theories-- with a rich history of study-- that we call `diskoseismology'. We also discuss other recent alternative theories, namely Lense-Thirring precession of tilted rings near the disc inner edge. We discuss the advantages and disadvantages of each of these theories, and discuss possible future directions for study.