Abstract: Graphdiyne is a new kind of two-dimensional carbonaceous material that is composed of sp and sp² hybridized carbon atoms. The highly conjugated and adjustable carbocyclic molecular structure gives it special physicochemical properties, which also facilitate its functional modification and wide application. In the past ten years, there has been extensive theoretical and experimental research on graphdiyne, and a series of important advances has been made in many fields. The properties of graphdiyne are briefly introduced, and its main synthesis methods with different morphologies are summarized, including Glaser-Hay cross-coupling, chemical vapor deposition, van der Waals epitaxial growth, thermal explosion, interface- confined synthesis and a bipolar electrochemical method. Theoretical calculations and experimental studies on non-metal and metal atom doping and chemical group modification are summarized, and their corresponding effects on the graphdiyne properties are reviewed. Finally, urgent problems and challenges in the development of graphdiyne are discussed. This review provides fundamental information on graphdiyne and guidance for the design of its functionalized forms.