Graphynes (GYs) are carbon allotropes with single-atom thickness that feature layered 2D structure assembled by carbon atoms with sp- and sp(2)- hybridization form. Various functional theories have predicted GYs to have natural band gap with Dirac cones structure, presumably originating from inhomogeneous pi-bonding between those carbon atoms with different hybridization and overlap of the carbon 2p(z) orbitals. Among all the GYs, graphdiyne (GDY) was the first reported to be prepared practically and, hence, attracted the attention of many researchers toward this new planar, layered material, as well as other GYs. Several approaches have been reported to be able to modify the band gap of GDY, containing invoking strain, boron/nitrogen doping, nanoribbon architectures, hydrogenation, and so on. GDY has been well-prepared in many different morphologies, like nanowires, nanotube arrays, nanowalls, nanosheets, ordered stripe arrays, and 3D framwork. The fascinating structure and electronic properties of GDY make it a potential candidate carbon material with many applications. It has recently revealed the practicality of GDY as catalyst; in rechargeable batteries, solar cells, electronic devices, magnetism, detector, biomedicine, and therapy; and for gas separation as well as water purification.