In recent years, bullying and aggression against users on social media have grown significantly, causing serious consequences to victims of all demographics. In particular, cyberbullying affects more than half of young social media users worldwide, and has also led to teenage suicides, prompted by prolonged and/or coordinated digital harassment. Nonetheless, tools and technologies for understanding and mitigating it are scarce and mostly ineffective. In this paper, we present a principled and scalable approach to detect bullying and aggressive behavior on Twitter. We propose a robust methodology for extracting text, user, and network-based attributes, studying the properties of cyberbullies and aggressors, and what features distinguish them from regular users. We find that bully users post less, participate in fewer online communities, and are less popular than normal users, while aggressors are quite popular and tend to include more negativity in their posts. We evaluate our methodology using a corpus of 1.6M tweets posted over 3 months, and show that machine learning classification algorithms can accurately detect users exhibiting bullying and aggressive behavior, achieving over 90% AUC.