Precise phase control of ultrashort optical pulse trains has produced remarkable and unexpected results in precision frequency spectroscopy and ultrafast science. The convergence of these seemingly disparate fields of physics over recent years due to the development of the optical frequency comb continues to facilitate new avenues of research. The phase stabilization of ultrafast mode-locked lasers has revolutionized the accurate measurement of optical frequencies and simultaneously provided precise control over the temporal oscillations of the optical field, opening new frontiers in ultrafast science and enabling studies of dynamical processes on attosecond time scales. We have recently demonstrated, for the first time, the extension of the optical frequency comb into the extreme-ultraviolet (EUV) portion of the spectrum. Utilizing a resonant optical cavity specifically designed to support femtosecond pulses we significantly increase the pulse energy from a standard mode-locked laser and produce high-order harmonics of the fundamental laser pulse (below 100 nm) at the full 100 MHz repetition frequency of the laser. Optical-heterodyne-based measurements reveal that the coherent frequency comb structure of the original laser is fully preserved in the high-harmonic generation process, with the phase variation measured to be less than 1 rad over a measurement time of 1 s. This approach can significantly improve the average power conversion efficiency while dramatically improving the spectral resolution of spectroscopy in the EUV. The presence of the frequency comb structure in the EUV and the extraordinary spectral resolution (and the related temporal coherence) of the high-harmonic light may enable similar revolutions in precision measurement, quantum control, and ultrafast science as has been recently witnessed in the visible region.