Transient stability assessment (TSA) has always been a fundamental means for ensuring the secure and stable operation of power systems. Due to the integration of new elements such as power electronics, electric vehicles and renewable power generations, dynamic characteristics of power systems are becoming more and more complex, which makes TSA an increasingly urgent task. Since traditional time-domain simulations and direct method cannot meet the actual operation requirements of power systems, data-driven TSA has attracted growing attention from both academia and industry. This paper makes a comprehensive review from the following four aspects: feature extraction and selection, model construction, online learning and rule extraction; and then, summarizes the challenges and prospects for future research; finally, draws the conclusions of this review. This review will be beneficial for relevant researchers to better understand the research status, key technologies, and existing challenges in the field.