As a rising star of carbon allotropes, graphynes (GYs) merely consist of sp- and sp(2)-hybridized carbon atoms, which endow them a large conjugated network and expanded 2D porous structure. With unique topological structure, GYs display unusual semiconducting properties, especially in the aspects of charge mobility and electron transport. Among the members of the GY family, only graphdiyne (GD) can be successfully synthesized in large quantities. The advanced properties of GD make it promising in various applications. Here, the recent progress in the synthesis of GD and GD-based composites is reviewed as well as their applications in photorelated and electrocatalytic applications. It is hoped that this Review will promote the development and applications of carbon chemistry.