Abstract: Time series are widely present in domains such as industry, finance, transportation, meteorology, and healthcare, where they hold significant analytical and practical value. However, missing values caused by human errors or unforeseen events often compromise the completeness of time series, thereby undermining the accuracy and reliability of subsequent analysis and decision-making. Incomplete time series typically exhibit complex temporal dependencies and inter-variable correlations, making effective imputation a challenging task. Deep learning methods, with their powerful modeling capabilities, have emerged as a promising solution to address these challenges and have become an active area of research. We provide a comprehensive review of incomplete time series imputation methods based on deep learning. The survey begins by introducing the relevant concepts and definitions, followed by a systematic categorization and analysis of representative methods, highlighting their core ideas and characteristics. Commonly used open-source datasets and evaluation metrics are then summarized, along with a well-designed experimental framework. The experiments evaluate 10 mainstream deep learning models in terms of imputation performance and efficiency under various conditions, including different missing scenarios, missing rates, variable dimensions, sequence lengths, and downstream task performance. We analyze the experimental results to derive comprehensive insights, then recommend appropriate imputation methods based on these findings. Finally, we discuss current research trends and future directions in this field, concluding the survey.