There are numerous applications that need to deal with a large graph, including bioinformatics, social science, link analysis, citation analysis, and collaborative networks. A fundamental query is to query whether a node is reachable from another node in a large graph, which is called a reachability query. In this survey, we discuss several existing approaches to process reachability queries. In addition, we will discuss how to answer reachability queries with the shortest distance, and graph pattern matching over a large graph.