In recent years, neural systems have demonstrated highly effective learning ability and superior perception intelligence. However, they have been found to lack effective reasoning and cognitive ability. On the other hand, symbolic systems exhibit exceptional cognitive intelligence but suffer from poor learning capabilities when compared to neural systems. Recognizing the advantages and disadvantages of both methodologies, an ideal solution emerges: combining neural systems and symbolic systems to create neural-symbolic learning systems that possess powerful perception and cognition. The purpose of this paper is to survey the advancements in neural-symbolic learning systems from four distinct perspectives: challenges, methods, applications, and future directions. By doing so, this research aims to propel this emerging field forward, offering researchers a comprehensive and holistic overview. This overview will not only highlight the current state-of-the-art but also identify promising avenues for future research.