Complex networks naturally exist in a wide diversity of real-world scenarios. Efficient complex network analysis technology has wide applications, such as community detection, link prediction, etc. However, most complex network analytics methods suffer high computation and space cost dealing with large-scale networks. Network representation learning is one of the most efficient methods to solve this problem. It converts high-dimensional sparse network information into low-dimensional dense real-valued vectors which can be easily exploited by machine learning algorithms. Simultaneously, it facilitates efficient computation for subsequent applications. The traditional network representation embeds the entity objects in the low dimensional Euclidean vector space, but recent work has shown that the appropriate isometric space for embedding complex networks with hierarchical or tree-like structures, power-law degree distributions and high clustering is the negatively curved hyperbolic space. This survey conducts a systematic introduction and review of the literature in hyperbolic representation learning for complex networks.