The ever-increasing amount of multimedia content on modern social media platforms are valuable in many applications. While the openness and convenience features of social media also foster many rumors online. Without verification, these rumors would reach thousands of users immediately and cause serious damages. Many efforts have been taken to defeat online rumors automatically by mining the rich content provided on the open network with machine learning techniques. Most rumor detection methods can be categorized in three paradigms: the hand-crafted features based classification approaches, the propagation-based approaches and the neural networks approaches. In this survey, we introduce a formal definition of rumor in comparison with other definitions used in literatures. We summary the studies of automatic rumor detection so far and present details in three paradigms of rumor detection. We also give an introduction on existing datasets for rumor detection which would benefit following researches in this area. We give our suggestions for future rumors detection on microblogs as a conclusion. Automatic Rumor Detection on Microblogs: A Survey