This talk introduces how to address a fundamental challenge in applying deep learning to power systems: developing neural network models that transfer across significant system changes, including networks with entirely different topologies and dimensionalities, without requiring training data from unseen reconfigurations. Despite extensive research, most ML-based approaches remain system-specific, limiting real-world deployment. This limitation stems from a dual barrier. First, topology changes shift feature distributions and alter input dimensions due to power flow physics. Second, reconfigurations redefine output semantics and dimensionality, requiring models to handle configuration-specific outputs while maintaining transferable feature extraction. To overcome this challenge, we introduce a Universal Graph Convolutional Network (UGCN) that achieves transferability to any reconfiguration or variation of existing power systems without any prior knowledge of new grid topologies or retraining during implementation. Our approach applies to both transmission and distribution networks and demonstrates generalization capability to completely unseen system reconfigurations, such as network restructuring and major grid expansions.  Experimental results across different power system applications, including false data injection detection and state forecasting, show that UGCN significantly outperforms state-of-the-art methods in cross-system zero-shot transferability of new reconfigurations.