Enigmatically, the incidence of deadly armed conflict on a world basis is declining, or at least remaining level, amid a prevailing, if not heightened, atmosphere of insecurity. The explanation for the correlation of more peace and less security lies in the rise of ‘hyperconflict.’ The prefix ‘hyper’ suggests excessive: in excess of plausible advances toward an enduring peace. Concretely, the concept of hyperconflict encompasses a reorganization of political violence, pervasive uncertainty, changing structures of various forms of conflict that are not necessarily in the hands of governments or their agents, and growing instability at the world level. This avenue of inquiry opens empirical and normative questions about evolving forms of global order. The analysis also points to transformative measures for achieving more peace, more security.