Online abusive content detection is an inherently difficult task. It has received considerable attention from academia, particularly within the computational linguistics community, and performance appears to have improved as the field has matured. However, considerable challenges and unaddressed frontiers remain, spanning technical, social and ethical dimensions. These issues constrain the performance, efficiency and generalizability of abusive content detection systems. In this article we delineate and clarify the main challenges and frontiers in the field, critically evaluate their implications and discuss potential solutions. We also highlight ways in which social scientific insights can advance research. We discuss the lack of support given to researchers working with abusive content and provide guidelines for ethical research.