Single-object tracking is a well-known and challenging research topic in computer vision. Over the last two decades, numerous researchers have proposed various algorithms to solve this problem and achieved promising results. Recently, Transformer-based tracking approaches have ushered in a new era in single-object tracking by introducing new perspectives and achieving superior tracking robustness. In this paper, we conduct an in-depth literature analysis of Transformer tracking approaches by categorizing them into CNN-Transformer based trackers, Two-stream Two-stage fully-Transformer based trackers, and One-stream One-stage fully-Transformer based trackers. In addition, we conduct experimental evaluations to assess their tracking robustness and computational efficiency using publicly available benchmark datasets. Furthermore, we measure their performances on different tracking scenarios to identify their strengths and weaknesses in particular situations. Our survey provides insights into the underlying principles of Transformer tracking approaches, the challenges they encounter, and the future directions they may take.INDEX TERMS Deep learning, tracking review, transformer tracking, vision transformer, visual object tracking.