The complexity and resilience of urban public transit network (PTN) are the interdisciplinary study area between transportation engineering and system science, which is a good demonstration of applying complex network theory to promote the development of engineering science. The deep understanding of this study helps to provide a new perspective for analyzing the reliability of urban PTN. Following study process of the complexity and resilience of complex network, this paper reviews the complexity and resilience of PTN from four topics, i.e., the PTN complexity, the static resilience of PTN, the dynamic resilience (cascading failures based resilience) of single layered PTN, and the dynamic resilience of interdependent PTN. In the literature review, multiple key items are, respectively, extracted for each topic, and the engineering applicability of each topic is also analyzed, which are both for obtaining the key features of this study area. Finally, in order to realize the development trend of cyclic and forward—complex network theory, network resilience theory, transforming into a realistic model and method that is close to actual public transit operation, engineering application and practice, and contributing to complex network theory, the study status is summarized and the future development trend is prospected.