Graph comparison is fundamentally important for many applications such as the analysis of social networks and biological data and has been a significant research area in the pattern recognition and pattern analysis domains. Nowadays, the graphs are large, they may have billions of nodes and edges. Comparison issues in such huge graphs are a challenging research problem. In this paper, we survey the research advances of comparison problems in large graphs. We review graph comparison and pattern matching approaches that focus on large graphs. We categorize the existing approaches into three classes: partition-based approaches, search space based approaches and summary based approaches. All the existing algorithms in these approaches are described in detail and analyzed according to multiple metrics such as time complexity, type of graphs or comparison concept. Finally, we identify directions for future research.