Single-cavity, dual-comb lasers are those specially designed mode-locked lasers that can emit more than one, asynchronous ultrashort pulse trains with stable repetition frequency difference between them. Unlike the long-studied, widely-used femtosecond lasers generating one stable pulse train, systematic investigation on them and their potential dual-comb applications only began, based on the fiber laser platform, around a decade ago, despite sporadic and limited reports of similar lasing phenomena since the beginning of the mode-locked laser studies. From a historic perspective, the birth of this novel technology is the lucky outcome of the timely collision of perpetual search for novel pulsing laser dynamics and concerted pursuit of open-minded solutions for out-of-lab dual-comb systems in the 2010s. In this review article, first, the current schemes to implement single-cavity dual optical frequency comb fiber lasers and their applications are summarized, based on the concept of multiplexed mode-locked lasers. The characteristics of reported single-cavity, dual-comb fiber lasers are discussed as well as their applications in spectroscopy, ranging, Terahertz (THz) spectroscopy, and asynchronous optical sampling (ASOPS). Finally, the more recent development of single-cavity, multi-comb lasers is presented.