In recent years, offensive, abusive and hateful language, sexism,  racism and other types of aggressive and cyberbullying behavior have  been manifesting with increased frequency, and in many online social  media platforms. In fact, past scientific work focused on studying  these forms in popular media, such as Facebook, Twitter, Instagram,  Ask.fm, etc. However, these platforms have not adequately addressed  the problem of online abusive behavior, and their responsiveness, as  well as effective detection and blocking of such inappropriate  behavior remain limited. In this talk, I will cover our recent works,  in which we propose a set of algorithms to detect and mitigate such  complex user behavior. In these studies, we collect, analyze and  annotate user content from Twitter, and employ advanced machine and  deep learning approaches to detect online aggressive behavior, in its  various facets. We use a diverse set of features, extracted from  textual, user and network-related activities of Twitter users, and  demonstrate that such characteristics can boost the algorithmic  performance for detection cyber-aggression. Furthermore, we make our  collected and annotated datasets and algorithms publicly available for  further research and development by the scientific community. This  research has been supported by the Marie Sklodowska Curie RISE EU  project, No 691025.