  Black hole and neutron star X-ray binary systems routinely show
quasi-periodic oscillations (QPOs) in their X-ray flux. Despite being strong,
easily measurable signals, their physical origin has long remained elusive.
However, recent observational and theoretical work has greatly improved our
understanding. Here, we briefly review the basic phenomenology of the different
varieties of QPO in both black hole and neutron star systems before focusing
mainly on low frequency QPOs in black hole systems, for which much of the
recent progress has been made. We describe the detailed statistical properties
of these QPOs and review the physical models proposed in the literature, with
particular attention to those based on Lense-Thirring precession. This is a
relativistic effect whereby a spinning massive object twists up the surrounding
spacetime, inducing nodal precession in inclined orbits. We review the theory
describing how an accretion flow reacts to the Lense-Thirring effect, including
analytic theory and recent numerical simulations. We then describe recent
observational tests that provide very strong evidence that at least a certain
type of low frequency QPOs are a geometric effect, and good evidence that they
are the result of precession. We discuss the possibility of the spin axis of
the compact object being misaligned with the binary rotation axis for a large
fraction of X-ray binaries, as is required for QPOs to be driven specifically
by Lense-Thirring precession, as well as some outstanding gaps in our
understanding and future opportunities provided by X-ray polarimeters and/or
high throughput X-ray detectors.
