FEL oscillator Ryan Lindberg Argonne National Laboratory A free-electron laser (FEL) oscillator operating at x-ray wavelengths has the potential to be a revolutionary science tool with x-ray properties that are complementary to FELs based on self-amplified spontaneous emission. In this talk I will start with the basic physics of x-ray FEL oscillators, including our understanding of the linear growth regime and the approach to nonlinear saturation and steady-state output. I will then proceed to briefly summarize recent experimental results that indicate that an x-ray FEL oscillator is technologically feasible, and then present how the full coherence of an XFELO may enable transferring many optical techniques, such as frequency comb generation, to the x-ray regime. Finally, I will close with a description of current research directions, including the optimization of electron beam sources and transport lines designed to drive an XFELO, analysis of an XFELO's tolerance to non-ideal effects, and the present open problem of determining the ultimate long-term stability limits of x-ray output in nonlinear saturation.