Severe mitral valve regurgitation (MR) is a heart valve disease that progresses to end-stage congestive heart failure and death if left untreated. Surgical repair or replacement of the mitral valve (MV) remains the gold standard for treatment of severe MR, with repair techniques aiming to restore the native geometry of the MV. However, patients with extensive co-morbidities may be ineligible for surgical intervention. With the emergence of transcatheter MV repair (TMVR) treatment paradigms for MR will evolve. The longer-term outcomes of TMVR and its effectiveness compared to surgical repair remain unknown given the differing patient eligibility for either treatment at this time. Advances in computational modeling will elucidate answers to these questions, employing techniques such as finite element method and fluid structure interactions. Use of clinical imaging will permit patient-specific MV models to be created with high accuracy and replicate MV pathophysiology. It is anticipated that TMVR technology will gradually expand to treat lower-risk patient groups, thus pre-procedural computational modeling will play a crucial role guiding clinicians towards the optimal intervention. Additionally, concerted efforts to create MV models will establish atlases of pathologies and biomechanics profiles which could delineate which patient populations would best benefit from specific surgical vs. TMVR options. In this review, we describe recent literature on MV computational modeling, its relevance to MV repair techniques, and future directions for translational application of computational modeling for treatment of MR.