Organ shortage is a major bottleneck in allotransplantation and causes many wait-listed patients to die or become too sick for transplantation. Genetically engineered pigs have been discussed as a potential alternative to allogeneic donor organs. Although xenotransplantation of pig-derived organs in nonhuman primates (NHPs) has shown sequential advances in recent years, there are still underlying problems that need to be completely addressed before clinical applications, including (i) acute humoral xenograft rejection; (ii) acute cellular rejection; (iii) dysregulation of coagulation and inflammation; (iv) physiological incompatibility; and (v) cross-species infection. Moreover, various genetic modifications to the pig donor need to be fully characterized, with the aim of identifying the ideal transgene combination for upcoming clinical trials. In addition, suitable pretransplant screening methods need to be confirmed for optimal donor-recipient matching, ensuring a good outcome from xenotransplantation. Herein, we summarize the understanding of organ xenotransplantation in pigs-to-NHPs and highlight the current status and recent progress in extending the survival time of pig xenografts and recipients. We also discuss practical strategies for overcoming the obstacles to xenotransplantation mentioned above to further advance transplantation of pig organs in the clinic.