The current paradigm of stroke risk assessment and mitigation in patients with atrial fibrillation (AF) is centred around clinical risk factors which, in the presence of AF, lead to thrombus formation. The mechanisms by which these clinical risk factors lead to thromboembolism, including any role played by atrial fibrosis, are not understood. In patients who had embolic stroke of undetermined source (ESUS), the problem is compounded by the absence of AF in a majority of patients despite long-term monitoring. Atrial fibrosis has emerged as a unifying mechanism that independently provides a substrate for arrhythmia and thrombus formation. Fibrosis-based computational models of AF initiation and maintenance promise to identify therapeutic targets in catheter ablation. In ESUS, fibrosis is also increasingly recognised as a major risk factor, but the underlying mechanism of this correlation is unclear. Simulations have uncovered potential vulnerability to arrhythmia induction in patients who had ESUS. Likewise, computational models of fluid dynamics representing blood flow in the left atrium and left atrium appendage have improved our understanding of thrombus formation, in particular left atrium appendage shapes and blood flow changes influenced by atrial remodelling. Multiscale modelling of blood flow dynamics based on structural fibrotic and morphological changes with associated cellular and tissue electrical remodelling leading to electromechanical abnormalities holds tremendous promise in providing a mechanistic understanding of the clinical problem of thromboembolisation. We present a review of clinical knowledge alongside computational modelling frameworks and conclude with a vision of a future paradigm integrating simulations in formulating personalised treatment plans for each patient.