The dual-comb spectroscopy (DCS) based on optical frequency combs (OFCs) offers a revolutionary new spectroscopic method that can combine the advantages of high spectral resolution, high detection sensitivity, broadband spectral coverage, and fast measurement in one. In the past few years, the DCS has experienced rapid development, resulting in numerous demonstrations of new measuring principles and implementation schemes, as well as the availability of new measuring technologies and applications. Therefore, it is necessary to systematically review the current development status for the DCS and predict its future trends objectively. To provide a reference for relevant scientific and technical personnel to grasp the whole development of DCS, based on the mechanism of asynchronous optical sampling and the noise properties, we begin with the OFC and provide a comprehensive review on research advances of DCS regarding measuring principles, implementation schemes, performance indexes, application technologies, and instrumentations, and predict possible development trends in the future.