In the big data era, much real-world data can be naturally represented as graphs. Consequently, many application domains can be modeled as graph processing. Graph processing, especially the processing of the large-scale graphs with the number of vertices and edges in the order of billions or even hundreds of billions, has attracted much attention in both industry and academia. It still remains a great challenge to process such large-scale graphs. Researchers have been seeking for new possible solutions. Because of the massive degree of parallelism and the high memory access bandwidth in GPU, utilizing GPU to accelerate graph processing proves to be a promising solution. This article surveys the key issues of graph processing on GPUs, including data layout, memory access pattern, workload mapping, and specific GPU programming. In this article, we summarize the state-of-the-art research on GPU-based graph processing, analyze the existing challenges in detail, and explore the research opportunities for the future.