Actinide nitride, as a potential nuclear fuel in future advanced nuclear energy system, has attracted much attention recently. Due to the chemical and radioactive toxicities of actinides, related experimental work are sometimes challenging. So it is of important significance to theoretically simulate and predict the structure and property evolution of actinide nitride fuels under various extreme conditions. Based on a large number of literature reports, with emphasis on our theoretical simulation results about actinide nitrides, here we selectively review the recent research progress on actinide nitrides by first-principles simulations, including the advancement of theoretical simulation methods, the ground state electronic properties, phase transition and the formation and diffusion behaviors of structural defects, so as to provide theoretical insights into further experimental endeavors on nitride nuclear fuels. In addition, this review also summarizes the key scientific issues which need to be solved or addressed in the study of actinide nitride.