Emergency responding requires effective interoperability, whereby different emergency teams combine efforts and expertise to contain and reduce the impact of an emergency. Within the United Kingdom, the capacity for the Emergency Services to be interoperable has been criticized by public enquiries. This systematic review had three goals to: (i) define interoperability; (ii) identify the structural principles that underpin interoperability and (iii) identify the psychological principles that outline how interoperability can be achieved. A PRISMA framework was used to identify 137 articles, including 94 articles from the systematic review, 15 articles from grey literature and 28 articles based on author expertise. We identified two structural principles of interoperability: (i) being able to communicate and exchange information effectively; and (ii) having a decentralized and flexible team network. We identified three psychological principles that informed how interoperability might be embedded in the team: (i) establishing trust between team members; (ii) developing secure team identities and (iii) building cohesive goals. We defined interoperability as a shared system of technology and teamwork built upon trust, identification, goals, communication and flexibility. Regular psychologically immersive training that targets these psychological principles will help to embed interoperability into the social fabric of multi‐team systems operating in high‐reliability organizations.