Optical frequency combs (OFCs) are a unique kind of light source, which are represented as a series of equally spaced coherent spectral lines in the frequency domain. OFCs can mainly be divided into mode-locked lasers, Kerr frequency combs, and electro-optic frequency combs (E-O combs), which have broad applications in optical communications, frequency metrology, atomic clocks, distance ranging, spectroscopy, and arbitrary waveform generation. Among them, E-O combs feature some unique advantages, such as fast tunable repetition rate, high sidebands power, and reconfigurability of the comb spectrum. Especially in recent years, with the development of micro-nano processing technology, on-chip E-O combs have become a dynamic research topic with many fundamental scientific problems as well as engineering applications for further exploration. To summarize the past development and envision the prosperous future of E-O combs, the area of E-O combs is reviewed from the following aspects: development of E-O combs; theory including the generation process of E-O combs and the electro-optic modulation models; important techniques including flattening, broadening, noise, and stability controlling; applications including communications, ranging, spectroscopy, wavelength calibration of astronomical spectrographs, and microwave generation; and pros and cons when compared with other OFCs.