Remotely sensed land surface temperature (LST) distribution has played a valuable role in land surface processes studies from local to global scales. However, it is still difficult to acquire concurrently high spatiotemporal resolution LST data due to the trade-off between spatial and temporal resolutions in thermal remote sensing. To address this problem, various methods have been proposed to enhance the resolutions of LST data, and substantial progress in this field has been achieved in recent years. Therefore, this study reviewed the current status of resolution enhancement methods for LST data. First, three groups of enhancement methods—spatial resolution enhancement, temporal resolution enhancement, and simultaneous spatiotemporal resolution enhancement—were comprehensively investigated and analyzed. Then, the quality assessment strategies for LST resolution enhancement methods and their advantages and disadvantages were specifically discussed. Finally, key directions for future studies in this field were suggested, i.e., synergy between process-driven and data-driven methods, cross-comparison among different methods, and improvement in localization strategy.