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Cavity-enhanced direct frequency comb spectroscopy combines broad spectralbandwidth, high spectral resolution, precise frequency calibration, andultrahigh detection sensitivity, all in one experimental platform based on anoptical frequency comb interacting with a high-finesse optical cavity. Precisecontrol of the optical frequency comb allows highly efficient, coherentcoupling of individual comb components with corresponding resonant modes of thehigh-finesse cavity. The long cavity lifetime dramatically enhances theeffective interaction between the light field and intracavity matter,increasing the sensitivity for measurement of optical losses by a factor thatis on the order of the cavity finesse. The use of low-dispersion mirrorspermits almost the entire spectral bandwidth of the frequency comb to beemployed for detection, covering a range of ~10% of the actual opticalfrequency. The light transmitted from the cavity is spectrally resolved toprovide a multitude of detection channels with spectral resolutions rangingfrom a several gigahertz to hundreds of kilohertz. In this review we willdiscuss the principle of cavity-enhanced direct frequency comb spectroscopy andthe various implementations of such systems. In particular, we discuss severaltypes of UV, optical, and IR frequency comb sources and optical cavity designsthat can be used for specific spectroscopic applications. We present severalcavity-comb coupling methods to take advantage of the broad spectral bandwidthand narrow spectral components of a frequency comb. Finally, we present aseries of experimental measurements on trace gas detections, human breathanalysis, and characterization of cold molecular beams.