The quality of welds during welding processes significantly affects the performance and the reliability of the final products. Therefore, to guarantee a high quality of the products, technologies that utilize time-series data measured by various sensors for monitoring the welding processes are required. Because the time-series data measured during the welding processes exhibit nonlinear and nonstationary characteristics, deep learning techniques, which can automatically learn the features of nonlinear and nonstationary signals through deep network structures, have recently gained recognition as a new monitoring method. Therefore, in this review, recent research that applied deep learning models based on time-series data measured during welding processes to monitor welding processes are introduced. In addition, the types of time-series data and deep learning model structures that are predominantly used to monitor the welding processes, such as predicting the penetration states and identifying the welding defects are discussed. Lastly, based on the research cases discussed herein, future research directions and the prospects of deep learning-based welding process monitoring technology that uses time-series data are discussed.