Comparative immunology: allorecognition and variable surface receptors outside the jawed vertebrates

•Adaptive immunity and allograft rejection are not unique to the jawed vertebrates.•Adaptive immunity and allograft rejection are separable in other organisms.•Rejection may be an inevitable consequence of the most diverse adaptive immune systems.•Systems intended to drive rejection do not resemble vertebrate immunity.

Allograft rejection is one of several undesirable consequences of the adaptive nature of the mammalian immune response. This review examines adaptive immune responses and allorecognition in animals with very different immune responses — jawless vertebrates, arthropods, and two distinct colonial marine invertebrates — with the goal of understanding how immune adaptation and allograft rejection are linked, and conversely how a system works where allograft rejection is a desired outcome rather than an unforeseen consequence.