Generative AI, including generative adversarial networks, diffusion models, variational approaches, and large language models, is increasingly being explored for smart-grid operation. Its appeal lies in its ability to create synthetic data, expand scenario sets, and support human operators facing complex and uncertain grid conditions. This review critically examines the state of generative AI in four key smart-grid applications: synthetic load profiles, contingency simulation, human-in-the-loop dispatch, and associated governance risks. It evaluates not only technical capability but also reliability, accountability, privacy, and operational readiness. A critical review of 28 peer-reviewed articles published between 2017 and 2026 is conducted. The selected literature is synthesized across methodological contributions, application domains, evaluation practices, and governance concerns. Generative AI shows promise in creating realistic load data and expanding contingency sets, but reliability, interpretability, and governance frameworks remain underdeveloped. Human-in-the-loop dispatch integration is still nascent, and most studies remain closer to proof-of-concept than operational deployment. While generative AI can enhance grid flexibility, simulation richness, and planning capability, its current maturity is uneven. Substantial research is needed to address technical, ethical, and regulatory challenges before these systems can be responsibly embedded in smart-grid operation.