An historical overview of laser-based, spectroscopic methods that employ high-finesse optical resonators is presented. The overview begins with the early work in atomic absorption (1962) and optical cavities (1974) that led to the first mirror reflectivity measurements in 1980. This paper concludes with very recent extensions of cavity-enhanced methods for the study of condensed-phase media and biological systems. Methods described here include cavity ring-down spectroscopy, integrated cavity output spectroscopy, and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Given the explosive growth of the field over the past decade, this review does not attempt to present a comprehensive bibliography of all work published in cavity-enhanced spectroscopy, but rather strives to illustrate the rich history, creative diversity, and broad applications potential of these methods.