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Foundation models are transforming artificial intelligence by enabling pre-training, adaptation, and reuse across heterogeneous tasks. Their application in energy systems is emerging rapidly, creating a need for systematic synthesis across forecasting, control, and decision-support settings. This systematic review identifies, categorizes, and evaluates the use of foundation models in energy-system forecasting, grid-edge control, and smart-grid decision support. It focuses on how large language models, pre-trained transformers, multi-modal models, and emerging time-series foundation models are adapted for energy tasks. A PRISMA-guided search of peer-reviewed literature from 2017 to 2025 resulted in 30 included studies. Models were classified by architecture, fine-tuning method, data modality, and application domain. The review finds that large language models dominate decision-support applications, while pre-trained transformers and time-series foundation models are most developed in forecasting. Grid-edge control applications remain nascent, with most studies addressing planning, diagnostics, or dispatch rather than closed-loop physical deployment. Foundation models hold significant promise for smart grids, but critical gaps remain in real-time control, safety assurance, privacy, and evaluation. A research agenda is proposed to guide rigorous, trustworthy, and operationally relevant deployment.