Cardiac digital twins are personalized virtual representations used to understand complex heart mechanisms. Solving the ECG inverse problem is crucial for accurate virtual heart modelling, enabling the derivation of internal electrical activity information from recorded surface potentials. Despite challenges from cardiac complexity, noisy ECG data, and computational efficiency, recent advancements hold significant promise for enhancing virtual heart modelling, ultimately advancing precision medicine in cardiology. This paper aims to provide a comprehensive review of the methods of solving ECG inverse problem, the validation strategies, the clinical applications, and future perspectives. For the computing methodologies, we broadly classify state-of-the-art approaches into two categories: deterministic and probabilistic methods, including conventional and deep learning-based techniques. Integrating physics laws with deep learning models holds promise, but challenges such as capturing dynamic electrophysiology accurately, accessing accurate domain knowledge, and quantifying prediction uncertainty persist. Integrating models into clinical workflows while ensuring interpretability and usability for healthcare professionals is essential. Overcoming these challenges will drive further research in cardiac digital twins.

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