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The rapid advancements in satellite remote sensing have enhanced the capability to monitor and analyze the Earth's surface. Among the many variables captured through satellite sensors, Land Surface Temperature (LST) plays a critical role in understanding key environmental processes. However, obtaining high-resolution LST data remains a challenge, as satellite sensors often face a trade-off between spatial and temporal resolutions. In response, Spatio-Temporal Fusion (STF) has emerged as a powerful method to integrate two satellite data sources, one providing high spatial but low temporal resolution, and the other offering high temporal but low spatial resolution. Although a range of STF techniques have been proposed, from traditional methods to cutting-edge deep learning (DL) models, most have focused on surface reflectance, with limited application to LST estimation. DL approaches, in particular, show promise in improving the spatial and temporal resolutions of LST by capturing complex, non-linear relationships between input and output LST data. This paper offers a comprehensive review of the latest advancements in DL-based STF techniques for LST estimation. We analyze key research developments, mathematically formulate the STF problem, and introduce a novel taxonomy for DL-based STF methods. Furthermore, we discuss the challenges faced by current methods and highlight future research directions. In addition, we present the first open-source benchmark STF dataset for LST estimation, consisting of 51 pairs of MODIS-Landsat images spanning from 2013 to 2024. To support our findings, we conduct extensive experiments on state-of-the-art methods and present both quantitative and qualitative assessments. This is the first survey paper focused on DL-based STF for LST estimation. We hope it serves as a valuable reference for researchers and paves the way for future research in this field., Comment: Submitted to the Proceedings of IEEE