One of the biggest challenges in graphene applications is how one can fabricate 3D architectures comprising graphene sheets in which the resulting architectures have inherited graphene's excellent intrinsic properties but have overcome its shortcomings. Two series of 3D graphene monoliths (GMs) using zigzag or armchair graphene nanoribbons as building blocks and sp(3) carbon chains as junction nodes are constructued, and calculations based on first principles are performed in order to predict their mechanical and electronic properties. The perfect match between sp(2) nanoribbons and sp(3) linkers results in favorable energy and mechanical/dynamic stability. Owing to their tailored motifs, wine-rack-like pores, and rigid sp(3) linkers, these GMs possess high surface areas, appreciable mechanical strength, and tunable band gaps. Negative linear compressibilities in a wide range are found for the zigzag GMs. By solving the problems of zero gap and dimensionality of graphene sheets simultaneously, these GMs offer a viable strategy towards many applications, e.g., microelectronic devices, energy storage, molecular sieves, sensitive pressure detectors, and telecommunication line systems.