The murder of George Floyd by a police officer in the United States in May 2020 and the subsequent turmoil, as well as the violence against migrants on the US-Mexican border, have drawn major public and media attention to the phenomenon of police brutality (see, e.g., Levin 2020; Misra 2018; Taub 2020), which is often labeled as ‘militarization of police’. At the same time, in recent years military forces have been increasingly involved in policing missions in civilian environments, both domestically (see, e.g., Kanno-Youngs 2020; Schrader 2020; Shinkman 2020) and abroad. The convergence of military conduct and policing raises intriguing questions regarding the impact of these tendencies on the military and the police, as well as on their legitimacy.