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The convergence of machine learning, high-throughput computation, and autonomous experimentation has transformed materials discovery into an AI-directed process capable of closed-loop, data-driven innovation at unprecedented speed. This narrative review examines the computational and data-driven materials engineering ecosystem, with a specific focus on the governance, regulatory, and institutional oversight frameworks required to steward these capabilities responsibly. We synthesize developments in materials informatics, representation learning, graph neural networks, active learning, uncertainty quantification, and simulation–experiment integration, showing how these tools have enabled autonomous laboratories and inverse design. Particular attention is given to community-driven calls for standards, explainability, and scientific responsibility that have emerged alongside the technology. By integrating technical literature with explicit discussions of data governance, reproducibility, and ethical deployment, we articulate the need for structured institutional oversight models that span standards bodies, regulatory readiness, and multi-stakeholder governance regimes. These models must operate at the infrastructure level—embedding accountability into discovery pipelines rather than retrofitting them. The review positions institutional oversight not as a constraint on innovation but as an essential enabler that ensures AI-directed materials engineering delivers safe, equitable, and societally beneficial outcomes.