Optical frequency comb consists of a series of equally spaced and highly stable frequency lines. Due to the advantages of the ultra-high frequency stability and ultra-low phase noise, the optical frequency combs have important applications in high precision spectroscopy, imaging, communications, etc. In the terahertz frequency range, semiconductor-based electrically pumped terahertz quantum cascade lasers have the characteristics of high output power and wide frequency coverage, and are the ideal candidates for generating terahertz optical frequency combs. In this article, we first briefly introduce the research progress of the optical frequency comb in the communication and the mid-infrared bands. Then we mainly review the research progress of the optical frequency combs based on the terahertz semiconductor quantum cascade laser (QCL) operating in free-running, active frequency stabilization and passive frequency stabilization modes. In free running mode, the terahertz QCL frequency comb is mainly limited by the large group velocity dispersion which results in a small comb bandwidth. Therefore, the dispersion compensation is one of the important methods to stabilize the optical frequency comb and broaden the spectral bandwidth. At present, the active frequency stabilization mode is a relatively matured method to realize the optical frequency combs in terahertz QCLs. In this article, we also detail the methods and applications of terahertz QCL dual-comb operations, including on-chip dual-comb and dual-comb spectroscopy. Compared with the Fourier transform infrared spectroscopy and time domain spectroscopy, the terahertz dual-comb spectroscopy has advantages in fast data acquisition (real-time) and high spectral resolution. The emergence of the dual-comb technique not only verifies the concept of optical frequency combs, but also further promotes the applications of frequency combs.