Laser-induced breakdown spectroscopy (LIBS) has the advantages of real-time, rapid, and multi-element simultaneous detection. It has attracted more and more attention in recent years and played an essential role in online industrial analysis. However, based on the emission spectrum characteristics, LIBS has spectral noise, baseline drift, self-absorption, and overlapping peaks, etc. In addition, spectral stability and reproducibility are poor due to environmental changes, laser energy fluctuations, matrix effects, and samples' surface topography. These result in the nonlinear relationship between spectral information and qualitative and quantitative analysis, limiting the analysis's sensitivity and accuracy. With the gradual improvement of LIBS devices' stability, LIBS spectral data analysis methods are also changing with each new day. Artificial neural networks (ANN) can track and identify nonlinear characteristics, adaptive learning of LIBS spectral characteristics, screening out interference information, and its application in LIBS data analysis has been rapidly developed. This paper introduces the principle, instrument structure, and working process of LIBS and common neural network model in the field of LIBS spectrum analysis, summed up the LIBS in 2015—2020 in combination with the common ANN model in geological, alloy and organic polymer, coal, soil and biological areas such as the specific application. It pointed out that ANN's super ability in the field of data analysis can effectively improve the LIBS analysis accuracy and improve the utilization rate of spectrum data, reducing the spectrum collection and environmental requirements. Given the technical difficulties that still required broken through, ANN's development prospect in LIBS spectral depth information mining, portable special equipment development, technology combination, and other aspects has prospected. LIBS is becoming more and more mature, but data analysis of this technology still has a broad space for development. This review can provide a reference for the application of machine learning in LIBS data analysis.