The mitral valve (MV) apparatus consists of the two asymmetric leaflets, the saddle-shaped annulus, the chordae tendineae, and the papillary muscles. MV function over the cardiac cycle involves complex interaction between the MV apparatus components for efficient blood circulation. Common diseases of the MV include valvular stenosis, regurgitation, and prolapse. MV repair is the most popular and most reliable surgical treatment for early MV pathology. One of the unsolved problems in MV repair is to predict the optimal repair strategy for each patient. Although experimental studies have provided valuable information to improve repair techniques, computational simulations are increasingly playing an important role in understanding the complex MV dynamics, particularly with the availability of patient-specific real-time imaging modalities. This work presents a review of computational simulation studies of MV function employing finite element structural analysis and fluid-structure interaction approach reported in the literature to date. More recent studies towards potential applications of computational simulation approaches in the assessment of valvular repair techniques and potential pre-surgical planning of repair strategies are also discussed. It is anticipated that further advancements in computational techniques combined with the next generations of clinical imaging modalities will enable physiologically more realistic simulations. Such advancement in imaging and computation will allow for patient-specific, disease-specific, and case-specific MV evaluation and virtual prediction of MV repair.