Some scholars and others are skeptical of a significant role for the Internet in processes of violent radicalization. There is increasing concern on the part of other scholars, and increasingly also policymakers and publics, that easy availability of violent extremist content online may have violent radicalizing effects. This article identifies a number of core questions regarding the interaction of violent extremism and terrorism and the Internet, particularly social media, that have yet to be adequately addressed and supplies a series of six follow-up suggestions, flowing from these questions, for progressing research in this area. These suggestions relate to (1) widening the range of types of violent online extremism being studied beyond violent jihadis; (2) engaging in more comparative research, not just across ideologies, but also groups, countries, languages, and social media platforms; (3) deepening our analyses to include interviewing and virtual ethnographic approaches; (4) up-scaling or improving our capacity to undertake big data collection and analysis; (5) outreaching beyond terrorism studies to become acquainted with, for example, the Internet Studies literature and engaging in interdisciplinary research with, for example, computer scientists; and (6) paying more attention to gender as a factor in violent online extremism.