The improvement of observation capabilities has expanded the scale of new data available for time domain astronomy research, and the accumulation of observational data continues to accelerate. However, traditional data analysis methods are difficult to fully tap the potential scientific value of all data.Therefore, in the current and future research on light curve analysis, it is inevitable to use artificial intelligence (AI) technology to assist in data analysis in order to obtain as many candidates as possible with scientific research goals. This survey reviews important developments in light curve analysis over the past years, summarizes the basic concepts in machine learning and their applications in light curve analysis and concludes perspectives and challenges for light curve analysis in the near future. The full exploration of light curves of variable celestial objects relies heavily on new techniques derived from promotion of machine learning and deep learning in the astronomical big data era. This article is categorized under:deep learning, light curve analysis, machine learning, variable 1 | INTRODUCTION Time domain astronomy (TDA) is promoted by new wide-field multi-epoch sky surveys, and it is a research area that studies characteristics of the target celestial object changing with time by the large data sets coming from sky survey (Vaughan, 2013), and it is a branch of astronomy that studies astronomical phenomena with time-varying characteristics. TDA requires a sufficient number of observations for the same target celestial object in a certain time scale, and fits the obtained time series data to form a light curve. Quantitatively analyze the changing laws of time series to obtain specific astroinformatics on the target celestial object. The variable astronomical phenomena originate from the movement of celestial objects or systems and their physical changes, such as supernovae, pulsars, exoplanets, active galactic nuclei, and gamma-ray bursts. The analysis and statistics of time-varying celestial objects are important means to study the formation and evolution of the universe, galaxies, and various celestial systems.Ce Yu and Kun Li authors are equally contributed to this study.