As a new member of carbon allotropes, graphdiyne (GDY) has the characteristics of being one-atom-thick with two-dimensional layers comprising sp and sp2 hybridized carbon atoms, and represents a trend in the development of carbon materials. Its unique chemical and electronic structures give GDY many unique and fascinating properties such as rich chemical bonds, highly conjugated and super-large π structures, infinitely distributed pores and high inhomogeneity of charge distribution. GDY has entered a period of rapid development, especially with the significant emergence of fundamental research and applied research achievements over the past five years. As one of the frontiers of chemistry and materials science, graphdiyne was listed in the Top 10 research areas in the 2020 Research Frontiers report and was jointly released in the Top 10 in the world by Clarivate and the Chinese Academy of Sciences. The research results have shown the great potential of GDY in the applications of energy, catalysis, environmental science, electronic devices, detectors, biomedicine and therapy, etc. Scientists are eager to explore and fully reveal the new properties, discover new scientific concepts and phenomena, discover the new conversion modes and mechanisms of GDY in photoelectricity, energy, and catalysis, etc., and build the important scientific value of new conversion devices. This review covers research on the foundation and application of GDY, such as the controlled preparation of new methods of GDY and GDY-based materials, studies on new mechanisms and properties in chemistry and physics, and the foundation and applications in energy, catalysis, photoelectric and devices.