A temporal graph, as a graph structure with time dimension, plays a more and more important role in query processing and mining of graph data. Different with the traditional static graph, structure of the temporal graph changes with the time series, that is to say the edge of temporal graph is activated by time. And each edge of the temporal graph has the label of recording time, which makes the temporal graph contain more information than the static graph, so the existing data query processing methods cannot be used in the temporal graph. Therefore how to solve the problem of query processing and mining on the temporal graph has attracted much attention of researchers. This paper summarizes the existing query processing and mining methods on temporal graphs. Firstly, this paper gives the application background and basic definition of temporal graph, and combs the existing three typical models which are used to model temporal graph in the existing works. Secondly, this paper introduces and analyzes the existing work on temporal graph from three aspects: graph query processing method, graph mining method and temporal graph management system. Finally, the possible research directions on temporal graph are prospected to provide reference for related research.