Frequency combs, spectra of phase-coherent equidistant lines often generated by mode-locked femtosecond lasers, have revolutionized time and frequency metrology [1,2]. In recent years, new frequency comb lasers, of a high compactness or even on-chip, have been demonstrated in the mid-infrared and THz regions of the electromagnetic spectrum. They include electrically pumped quantum cascade and interband cascade semiconductor devices, as well as highquality factor microresonators. These new comb generators open up novel opportunities for spectroscopy of molecular fingerprints over broad spectral bandwidths: their small form-factor promises chip-scale spectrometers, while their large line spacing simplifies the resolution of the individual comb lines with simple spectrometers and provides short measurement times, with an intriguing potential for time-resolved spectroscopy in the condensed phase. This Letter summarizes the recent advances in this rapidly developing domain of on-chip combs for broadband spectroscopy and discusses some of the challenges and prospects. While some review articles already provide a perspective into some aspects of chip-based frequency comb generators [3][4][5], of mid-infrared frequency comb synthesizers [6] and of the applications of frequency combs to spectroscopy [7], the growing and rapidly advancing interest in molecular sensing using quantum cascade and microresonator-based on-chip frequency combs motivates this Letter.