Left ventricular assist devices (LVADs) are safer and provide better survival and better quality of life than biventricular assist devices (BVADs) but end-stage heart failure often involves both ventricles, even if its initial cause was left-sided heart disease. Right ventricular failure (RVF) is also a severe complication in about 25% of patients receiving an LVAD, with high perioperative morbidity (renal, hepatic or multi-organ failure) and mortality. Patients who receive an RV assist device (RVAD) only days after LVAD insertion fare much worse than those who receive an RVAD simultaneously with LVAD implantation. Temporary RVAD support in LVAD recipients with high risk for postoperative RVF can avoid permanent BVAD support. Thus, patients who definitely need a BVAD should already be identified preoperatively or at least intra-operatively. However, although the initial biochemical, hemodynamic and echocardiographic patient profiles at admission may suggest the need for a BVAD, many risk factors may be favorably modified by various strategies that may result in avoidance of RVF after LVAD implantation. This article summarizes the knowledge of risk factors for irreversible RVF after LVAD implantation and strategies to optimize RV function (preoperatively, intra-operatively and post-operatively) aimed to reduce the number of BVAD implantations. Special attention is focused on assessment of RV size, geometry and function in relation to loading conditions with the goal of predicting preoperatively the RV changes which might be induced by RV afterload reduction with the LVAD. The review also provides a theoretical and practical basis for clinicians intending to be engaged in this field.