PURPOSE OF REVIEW: The generation of pigs lacking Galalpha1,3Gal (alphaGal) or overexpressing human regulators of complement has largely overcome the barrier of hyperacute xenograft rejection. Nevertheless, delayed xenograft rejection remains a major hurdle, including humoral responses against nonalphaGal epitopes, and cellular innate immune responses. This review addresses the early interactions between the porcine endothelium and human natural killer cells, neutrophils, and monocytes/macrophages. RECENT FINDINGS: Whether human leukocyte recruitment to, and lysis of, porcine endothelial cells includes direct recognition of alphaGal remains a matter of debate. Although the human natural killer receptor natural killerRP1A may directly recognize alphaGal, several studies did not reveal significant differences regarding adhesion, transmigration, and cytotoxicity using porcine endothelial cells expressing or lacking alphaGal. The strong human monocyte response against pig cells partly relies on the inability of porcine ligands to ligate inhibitory human receptors, such as SIRPalpha. Strategies to overcome cellular innate immune responses include transgenic expression in porcine cells of human ligands for inhibitory receptors, together with species-specific blocking of porcine ligands mediating human leukocyte interactions. SUMMARY: Cellular human innate immune responses are increasingly recognized as barriers to successful pig-to-human xenotransplantation, and only a detailed knowledge of the molecular mechanisms involved will allow us to overcome this barrier.