Artificial Intelligence (AI) is transforming every aspect of modern society. It demonstrates a high potential to contribute to more flexible operations of safety-critical network infrastructures under deep transformation to tackle global challenges, such as climate change, energy transition, efficiency, and digital transformation, including increasing infrastructure resilience to natural and human-made hazards. The widespread adoption of AI creates the conditions for a new and inevitable interaction between humans and AI-based decision systems. In such a scenario, creating an ecosystem in which humans and AI interact healthily, where the roles and positions of both actors are well-defined, is a critical challenge for research and industry in the coming years. This perspective article outlines the challenges and requirements for effective human-AI interaction by taking an interdisciplinary point of view that merges computer science, decision-making sciences, psychological constructs, and industrial practices. The work focuses on three emblematic safety-critical scenarios from two different domains: energy (power grids) and mobility (railway networks and air traffic management).