The rise of online aggression on social media is evolving into a major point of concern. Several machine and deep learning approaches have been proposed recently for detecting various types of aggressive behavior. However, social media are fast paced, generating an increasing amount of content, while aggressive behavior evolves over time. In this work, we introduce the first, practical, real-time framework for detecting aggression on Twitter via embracing the streaming machine learning paradigm. Our method adapts its ML classifiers in an incremental fashion as it receives new annotated examples and is able to achieve the same (or even higher) performance as batch-based ML models, with over 90% accuracy, precision, and recall. At the same time, our experimental analysis on real Twitter data reveals how our framework can easily scale to accommodate the entire Twitter Firehose (of 778 million tweets per day) with only 3 commodity machines. Finally, we show that our framework is general enough to detect other related behaviors such as sarcasm, racism, and sexism in real time.