Rumor detection on online social network (OSN) aims to help people retrieve reliable information and prevent public panic when emergencies occur suddenly. However, it is a waste of human efforts to detect rumors from the rapid growth of large-scale datasets. Due to the development of artificial intelligence, many architectures and frameworks are proposed to provide solutions for this issue. The first proposed traditional feature related methods are time-consuming and heavily depend on well-designed features, which calls for novel methods to detect rumors more efficiently. Thus deep neural networks related methods are successively born, and recent research on propagation related methods has captured much attention of both academia and industry. However, there lacks a systematic and global survey in the field of modern rumor detection. In this paper, we introduce rumors and OSN, and then present a comprehensive study of rumor detection methods on OSN, classifying them according to their search approaches and providing a comparison of the selected works. Finally, this survey deliver unique views on key challenges and several future research directions of rumor detection on OSN, such as multi-task learning, multi-modal detection and developing standard datasets and benchmarks. This work is supported by the Department of System Science, College of Liberal Arts and Sciences in National University of Defense Technology.