Heat source-induced thermal error is a primary element influencing the precision of CNC machine tools. A practical and economical approach to mitigating thermal errors is through thermal error compensation. To provide a comprehensive understanding of thermal error modeling and its advancements, this paper systematically reviews machine learning-based methods for thermal error compensation. Thermal error modeling is the most critical step in thermal error compensation, as it directly influences the effectiveness of the compensation due to its accuracy and robustness. With the rapid development of big data and artificial intelligence, machine learning has emerged as a powerful tool in thermal error modeling, leading to significant research progress in recent years. In this paper, an overview of the thermal error modeling methods based on deep learning that have been researched and applied in recent years is presented. Specifically, two methods for reducing thermal errors, namely, thermal error suppression and thermal error compensation, are introduced and analyzed. Second, machine learning-based thermal error modeling methods are categorized into traditional machine learning-driven and deep learning-driven approaches. The application of these two methods in thermal error modeling and compensation is reviewed and summarized in detail. By synthesizing these studies, this paper identifies key challenges and trends in machine learning-based thermal error modeling. Finally, the thermal error modeling methods discussed in this paper are summarized, and future research directions are proposed to further enhance modeling accuracy and robustness.