In the current era of online interactions, both positive and negative experiences are abundant on the Web. As in real life, negative experiences can have a serious impact on youngsters. Recent studies have reported cybervictimization rates among teenagers that vary between 20% and 40%. In this paper, we focus on cyberbullying as a particular form of cybervictimization and explore its automatic detection and fine-grained classification. Data containing cyberbullying was collected from the social networking site Ask.fm. We developed and applied a new scheme for cyberbullying annotation, which describes the presence and severity of cyberbullying, a post author's role (harasser, victim or bystander) and a number of fine-grained categories related to cyberbullying, such as insults and threats. We present experimental results on the automatic detection of cyberbullying and explore the feasibility of detecting the more fine-grained cyberbullying categories in online posts. For the first task, an F-score of 55.39% is obtained. We observe that the detection of the fine-grained categories (e.g. threats) is more challenging, presumably due to data sparsity, and because they are often expressed in a subtle and implicit way.