Graphdiyne (GDY), a two-dimensional allotrope of graphene, was first synthesized in 2010 and has attracted attention as a new low-dimensional carbon material. This work surveys the literature on GDYs. The history of GDYs is summarized, including their relationship with two-dimensional graphyne carbons and yearly publication trends. GDY is a molecule-based nanosheet woven from a molecular monomer, hexaethynylbenzene; thus, it is synthesized by bottom-up approaches, which allow rich variation via monomer design. The GDY family and the synthetic procedures are also described. Highly developed -conjugated electronic structures are common important features in GDY and graphene; however, the coexistence of sp and sp 2 carbons differentiates GDY from graphene. This difference gives rise to unique physical properties, such as high conductivity and large carrier mobility. Next, the theoretical and experimental studies of these properties are described in detail. A wide variety of applications have been proposed for GDYs, including electrocatalysts and energy devices, which exploit the carbon-rich nature, porous framework, and expanded -electron system of these compounds. Finally, potential uses are discussed.