Current X-ray Free-Electron Lasers (XFELs), like SACLA at RIKEN, or the LCLS at SLAC,
are single-pass X-ray light sources, where electrons produce X-rays as they pass through an
undulator line just once. The exponential gain of X-ray power in an XFEL occurs as X-rays
act on the electron beam, causing it to form microbunches at the X-ray wavelength. In a
single-pass SASE (self-amplified spontaneous emission) XFEL, the X-rays which initiate this
process come from noise in the beam, and thus X-rays produced by current XFELs are
transversely coherent, but longitudinally noisy. In proposed cavity-based XFELs
(CBXFELs) [1], by contrast, X-rays are returned by mirrors from the end of the undulator
line to the beginning, so a strong X-ray pulse is used to seed the FEL process on subsequent
passes. Future X-ray light sources based on CBXFELs can thus produce longitudinally
coherent pulses with improved spectral brightness, and promise to be more stable than current
XFELs. This talk will give an overview of CBXFELs and show recent progress towards
constructing them, including demonstration of a 14 meter hard X-ray cavity at LCLS.