Optical frequency comb is widely used in high precision measurement and metrology because of its characteristics such as constant frequency interval, wavelength stability, narrow spectral line width and wide spectral band width. Among them, the fast dual-comb measurement, including spectroscopy, absolute ranging, 3D imaging and ultra fast asynchronous optical sampling, has become one of the research hotspots. The dual-comb spectroscopy system based on free-running single-cavity dual-comb laser has attracted much attention due to its advantages of simple structure, large measurement range and high accuracy. This article first introduces the features of the optical frequency comb in the time domain and frequency domain andits application, especially the advantages of the dual-comb measurement. Compared with the current mainstream dual-comb source schemes, such as frequency-stabilized and phase-locked mode-locked laser, electro-optic modulation and so on, the single-cavity dual-comb laser scheme is expected to avoid the use of complex electronic control system and simplify the structure and decrease the volume and the cost of the dual-comb source. Therefore, this paper mainly introduces single-cavity dual-comb fiber laser technology with wavelength-multiplexing, polarization-multiplexing, space-multiplexing and pulse-shape-multiplexing, and analyzes the basic principles, performance parameters and current research progress, as well as the existing problems in the current development of these technologies. Moreover, the researches and performances of polarization-maintaining fiber dual-comb lasers with higher stability are summarized. Then, this paper introduces the principle of dual-comb spectroscopy, reviews the current spectral extension technology, and introduces some application cases of dual-comb spectroscopy based on the free-running single-cavity dual-comb laser in detail, including the near infrared band of the erbium-doped fiber laser and the detection extended to mid-infrared and terahertz bands. Finally, we summarize the development trends of single-cavity dual-comb lasers, including further improving frequency stability of single-cavity dual-comb lasers, decreasing the common-mode noise of single-cavity lasers, exploring the application of single-cavity dual-comb system in mid-infrared and terahertz band, and making single-cavity dual-comb mode-locked fiber laser to be practical.