The current review addresses emerging issues that arise from the creation of safe, beneficial, and trusted artificial intelligence–air traffic controller (AI-ATCO) systems for air traffic management (ATM). These issues concern trust between the human user and automated or AI tools of interest, resilience, safety, and transparency. To tackle these issues, we advocate the development of practical AI ATCO teaming frameworks by bringing together concepts and theories from neuroscience and explainable AI (XAI). By pooling together knowledge from both ATCO and AI perspectives, we seek to establish confidence in AI-enabled technologies for ATCOs. In this review, we present an overview of the extant studies that shed light on the research and development of trusted human-AI systems, and discuss the prospects of extending such works to building better trusted ATCO-AI systems. This paper contains three sections elucidating trust-related human performance, AI and explainable AI (XAI), and human-AI teaming.