Researching how hate speech emerges and spreads and how it is regulated offers a unique lens to understand how different traditions understand speech and its limits. Earlier studies have focused on the deep divergence separating European and American approaches towards regulation, but the realization that the most dire consequences of speech inciting hatred are felt not in relatively stable democracies, but in fragile and transitioning societies has led to calls for more empirically grounded research, trying to understand how hate speech emerges and spreads in different sociocultural contexts, and how online speech can provoke offline violence. By focusing on online hate speech, this chapter first offers an overview of the challenges of defining and responding to hate speech, as further exacerbated by the proliferation of social media and by the opportunities they provide to myriad users to post anonymously, across jurisdictions, and in ways that tend to make hateful remarks more visible and permanent. In the second half, the chapter provides concrete examples of how empirical research can help address some definitional challenges, leading to a better understanding of how different online practices are connected to specific cultures of communication, and to more grounded, and possibly more effective, responses to speech that can lead to violence.