Based on atomic emission spectrometry, laser-induced breakdown spectroscopy (LIBS) is a convenient and sensitive spectroscopic technique for the qualitative and quantitative element analysis. With the development of laser technique and spectrum analysis instrument, the technology and applications of LIBS have been rapidly developed. Beginning with the fundamental and working principle of the general LIBS, we present an overview of the recent progress of nanosecond LIBS in the technical development of portable and standoff systems and in its applications in environment monitoring, food safety, biological medicine, archaeology, space exploration and isotopic identification. The advantages of femtosecond LIBS and its recent applications are discussed. The principle and application progress of femtosecond laser filament induced breakdown spectroscopy are summarized.