The management of decentralized energy resources and smart grids needs novel data-driven low-latency applications and services to improve resilience and responsiveness and ensure closer to real-time control. However, the large-scale integration of Internet of Things (IoT) devices has led to the generation of significant amounts of data at the edge of the grid, posing challenges for the traditional cloud-based smart-grid architectures to meet the stringent latency and response time requirements of emerging applications. In this paper, we delve into the energy grid and computational distribution architectures, including edge–fog–cloud models, computational orchestration, and smart-grid frameworks to support the design and offloading of grid applications across the computational continuum. Key factors influencing the offloading process, such as network performance, data and Artificial Intelligence (AI) processes, computational requirements, application-specific factors, and energy efficiency, are analyzed considering the smart-grid operational requirements. We conduct a comprehensive overview of the current research landscape to support decision-making regarding offloading strategies from cloud to fog or edge. The focus is on metaheuristics for identifying near-optimal solutions and reinforcement learning for adaptively optimizing the process. A macro perspective on determining when and what to offload in the smart grid is provided for the next-generation AI applications, offering an overview of the features and trade-offs for selecting between federated learning and edge AI solutions. Finally, the work contributes to a comprehensive understanding of edge offloading in smart grids, providing a Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis to support cost–benefit analysis in decision-making regarding offloading strategies.