Solid oxide cells (SOCs) are a cornerstone technology for sustainable energy conversion, enabling efficient, bidirectional transformation between electrical and chemical energy. However, large-scale deployment is constrained by complex, multi-scale electrochemical-thermal-mechanical processes, rendering accurate modeling and real-time control computationally prohibitive. Traditional physics-based models (e.g., CFD, FEA) offer high-fidelity but are costly and inflexible, whereas purely data-driven models lack physical interpretability and generalization under out-of-distribution conditions. To bridge this gap, the emerging paradigm of physics-informed artificial intelligence integrates physical laws, governing equations, and mechanistic knowledge into machine learning frameworks, thereby achieving a balance between physical consistency, computational efficiency, and data adaptability. This review provides a systematic synthesis of physics-informed artificial intelligence methodologies in the solid oxide cells domain and introduces a hierarchical taxonomy encompassing three progressively integrated paradigms: loss-level physics injection, architecture-level fusion, and integration-level correction. These paradigms reflect an evolution from externally constrained learning to fully coupled hybrid intelligence, aligning with the increasing complexity of solid oxide cells modeling and digital twins deployment. Representative applications across microstructural evolution, stack-level performance mapping, degradation diagnosis, and optimization are analyzed to illustrate how physics-informed artificial intelligence enhances interpretability, robustness, and scalability in practical solid oxide cells workflows. Finally, the review identifies key challenges—such as spectral bias, multi-fidelity data fusion, and uncertainty quantification—and highlights emerging directions including neural operators, Bayesian deep learning, and hybrid digital twins architectures to accelerate the physics-artificial intelligence convergence toward reliable, real-time, and lifecycle-aware solid oxide cells engineering.