We argue that existing security, privacy, and anti-abuse protections fail to address the growing threat of online hate and harassment. In order for our community to understand and address this gap, we propose a taxonomy for reasoning about online hate and harassment. Our taxonomy draws on over 150 interdisciplinary research papers that cover disparate threats ranging from intimate partner violence to coordinated mobs. In the process, we identify seven classes of attacks—such as toxic content and surveillance—that each stem from different attacker capabilities and intents. We also provide longitudinal evidence from a three-year survey that hate and harassment is a pervasive, growing experience for online users, particularly for at-risk communities like young adults and people who identify as LGBTQ+. Responding to each class of hate and harassment requires a unique strategy and we highlight five such potential research directions that ultimately empower individuals, communities, and platforms to do so.