Antibodies targeting CD38 are rapidly changing the treatment landscape of multiple myeloma (MM). CD38−directed antibodies have several mechanisms of action. Fc−dependent immune effector mechanisms include complement-dependent cytotoxicity (CDC), antibody−dependent cell−mediated cytotoxicity (ADCC), antibody-dependent cellular phagocytosis (ADCP) and apoptosis. In addition, direct effects and immunomodulatory effects contribute to the efficacy of CD38−directed antibodies. Daratumumab, the first−in−class anti−CD38 monoclonal antibody, is now part of standard treatment regimens of both newly diagnosed as well as relapsed/refractory MM patients. The FDA has recently approved isatuximab in combination with pomalidomide and dexamethasone for relapsed/refractory MM patients after at least two prior therapies. Further, the other CD38−targeting antibodies (i.e., MOR202 and TAK-079) are increasingly used in clinical trials. The shift to front-line treatment of daratumumab will lead to an increase in patients refractory to CD38 antibody therapy already after first−line treatment. Therefore, it is important to gain insight into the mechanisms of resistance to CD38−targeting antibodies in MM, and to develop strategies to overcome this resistance. In the current review, we will briefly describe the most important clinical data and mechanisms of action and will focus in depth on the current knowledge on mechanisms of resistance to CD38-targeting antibodies and potential strategies to overcome this.