Filter bank frame is one of the most important topics in applied mathematics, signal processing, image processing and digital communication. The analysis and design of filter bank frames have great scientific significance and practical merits. In recent years, with the emergence of high-dimensional data in irregular domains, many scholars began studying the filter bank methods in graph signals processing. In this paper, we review the filter bank theory and its applications in graph signal processing. After a brief introduction on the background knowledge of filter banks and frames, we summarize various methods in the analysis and design of filter bank frames. Then we present in detail two frameworks of graph signal processing and the state-of-the-art research on graph filter banks. Finally, some interesting problems of the future research are discussed.