The remodeling that occurs after a posterolateral myocardial infarction can alter mitral valve function by creating conformational abnormalities in the mitral annulus and in the posteromedial papillary muscle, leading to mitral regurgitation (MR). It is generally assumed that this remodeling is caused by a volume load and is mediated by an increase in diastolic wall stress. Thus, MR can be both the cause and effect of an abnormal cardiac stress environment. Computational modeling of ischemic MR and its surgical correction is attractive because it enables an examination of whether a given intervention addresses the correction of regurgitation (fluid-flow) at the cost of abnormal tissue stress. This is significant because the negative effects of an increased wall stress due to the intervention will only be evident over time. However, a meaningful fluid–structure interaction (FSI) model of the left heart is not trivial; it requires a careful characterization of the in vivo cardiac geometry, the tissue parameterization through inverse analysis, a robust coupled solver that handles collapsing Lagrangian interfaces, the automatic grid-generation algorithms that are capable of accurately discretizing the cardiac geometry, the innovations in image analysis, the competent and efficient constitutive models and an understanding of the spatial organization of tissue microstructure. In this paper, we profile our work toward a comprehensive FSI model of the left heart by reviewing our early work, presenting our current work and laying out our future work in four broad categories: data collection, geometry, FSI and validation. Copyright © 2009 John Wiley & Sons, Ltd.