This paper reviews recent advances in the double-graphene-layer (DGL) active plasmonic heterostructures for the terahertz (THz) device applications. The DGL consists of a core shell in which a thin tunnel barrier layer is sandwiched by the two GLs being independently connected with the side contacts and outer gate stack layers at both sides. The DGL core shell works as a nano-capacitor, exhibiting inter-GL resonant tunneling (RT) when the band offset between the two GLs is aligned. The RT produces a strong nonlinearity with a negative differential conductance in the DGL current-voltage characteristics. The excitation of the graphene plasmons by the THz radiation resonantly modulates the tunneling currentvoltage characteristics. When the band offset is aligned to the THz photon energy, the DGL structure can mediate photonassisted RT, resulting in resonant emission or detection of the THz radiation. The cooperative double-resonant excitation with structure-sensitive graphene plasmons gives rise to various functionalities such as rectification (detection), photomixing, higher harmonic generation, and self-oscillation, in the THz device implementations.