We propose the far-infrared and terahertz emitting diodes (FIR-EDs and THz-EDs) based on the graphene-layer/black phosphorus (GL/b-P) and graphene-layer/MoS2 (GL/MoS2) heterostructures with the lateral hole and vertical electron injection and develop their device models. In these EDs, the GL serves as an active region emitting the FIR and THz photons. Depending on the material of the electron injector, the carriers in the GL can be either cooled or heated dictated by the interplay of the vertical electron injection and optical phonon recombination. The proposed EDs based on GL/b-P heterostructures can be efficient sources of the FIP and THz radiation operating at room temperature.