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Time-Sensitive Networking (TSN) is a set of standards that provide low-latency, high-reliability guarantees for the transmission of traffic in networks, and it is becoming an accepted solution for complex time-critical systems such as those in industrial automation and the automotive. In time-critical systems, it is essential to verify the timing predictability of the system, and the application of scheduling mechanisms in TSN can also bring about changes in system timing. Therefore, schedulability analysis techniques can be used to verify that the system is scheduled according to the scheduling mechanism and meets the timing requirements. In this paper, we provide a clear overview of the state-of-the-art works on the topic of schedulability analysis in TSN in an attempt to clarify the purpose of schedulability analysis, categorize the methods of schedulability analysis and compare their respective strengths and weaknesses, point out the scheduling mechanisms under analyzing and the corresponding traffic classes, clarify the network scenarios constructed during the evaluation and list the challenges and directions still needing to be worked on in schedulability analysis in TSN. To this end, we conducted a systematic literature review and finally identified 123 relevant research papers published in major conferences and journals in the past 15 years. Based on a comprehensive review of the relevant literature, we have identified several key findings and emphasized the future challenges in schedulability analysis for TSN.