Background: Myocardial infarction (MI) produces regionally heterogeneous loss of contractility and progressive extracellular matrix remodeling that reshapes left ventricular mechanics from hours to months. This review links infarct, border zone, and remote myocardium microstructure to organ-scale remodeling and patient-specific finite-element and growth-and-remodeling models. Methods: We synthesise experimental, computational, and translational studies on post-MI constitutive behavior, imaging-informed personalization, and inverse inference, emphasizing parameter identifiability and uncertainty quantification. Results: Contemporary models can reproduce volumes and strain patterns and support counterfactual simulations, but decision-grade prediction is limited by weak in vivo observability of regional stiffness and contractility, confounding with loading, and incomplete treatment of measurement and model-form uncertainty. Conclusions: Clinically credible prediction will require simplified, context-of-use-aligned models constrained by microstructure-informed priors, paired pressure-volume-strain datasets, longitudinal validation, and routine reporting of identifiability and uncertainty.