Graphynes (GYs) are a series of artificial carbon allotropes composed of sp- and sp2-hybridized carbon atoms. Although theoretical studies predict many possible GY structures, synthesizing them as real materials is extremely challenging. Among a few synthesized GYs, γ-GY has attracted extensive research interest over the past decade because it is predicted to possess fascinating properties such as direct bandgap, tunable electronic structure, high carrier mobility, two-dimensional ultrathin nature, and nanoporosity. This review first describes the structures and intrinsic properties of γ-GY predicted using theoretical calculations and introduces its potential applications based on the predicted properties. Further, this review summarizes the reported synthesis methods of γ-GY, including mechanochemical synthesis, Sonogashira coupling, Castro–Stephens coupling, and alkyne metathesis, and discusses their advantages and limitations. The material quality of γ-GY synthesized by each method is evaluated according to characterization results. Finally, this review outlines the challenges and opportunities in this field, critically highlighting that at present, most of the synthesized γ-GY materials lack long-range structural order and precise control over the layer number, defects, and impurities. As the synthesis of a well-defined high-quality material is the basis for reliable mechanistic and performance studies, this review aims to inspire the development of more efficient synthesis methods for γ-GY and other types of GYs.