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The rapid evolution of computational and data-driven materials engineering has ushered in autonomous discovery systems that integrate machine learning, high-throughput simulations, and robotic experimentation to accelerate materials innovation. Central to these systems are decision authority frameworks, which define how authority is delegated between human operators and artificial intelligence agents, ensuring safe, ethical, and efficient operations. This review synthesizes recent literature on delegation models, human override mechanisms, responsibility assignment, and policy encoding within materials informatics ecosystems. We examine how these frameworks operate in closed-loop discovery pipelines, where active learning and uncertainty quantification guide iterative experimentation. Key areas include representation learning via graph neural networks for materials property prediction, multimodal dataset integration for simulation-experiment synergy, and inverse design strategies that balance exploration and exploitation. By analyzing delegation in autonomous laboratories, we highlight the role of human-in-the-loop paradigms in mitigating risks such as algorithmic bias or experimental failures. The review underscores the need for robust policy encodings that embed ethical constraints and regulatory compliance into AI-driven workflows. Drawing from high-impact studies, we provide an integrative perspective on how these frameworks enhance reliability in materials discovery, paving the way for scalable, trustworthy autonomous systems in computational materials science.