  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.
