Among all the 2D-carbon materials, graphyne is currently one of the most interesting carbon allotropes besides graphene. It has potential applications in a wide variety of scientific fields owing to its unique sp-sp2 hybrid network, which endows desirable electronic properties towards energy-related applications. In this review, we summarize the recent progress in graphynes for electronic and energy applications from a theoretical point of view. The intrinsic electronic structure of graphyne and its chemical and mechanical properties are comprehensively described. It is hoped that this review could provide a strong theoretical understanding of graphynes, thus accelerating the design of robust and efficient graphyne-based advanced energy and electronic devices in the future.