This paper proposes a Generative Face Video Compression (GFVC) approach using Supplemental Enhancement Information (SEI), where a series of compact spatial and temporal representations of a face video signal (i.e., 2D/3D key-points, facial semantics and compact features) can be coded using SEI message and inserted into the coded video bitstream. At the time of writing, the proposed GFVC approach is an official "technology under consideration" (TuC) for standardization by the Joint Video Experts Team (JVET) of ISO/IEC JVT 1/SC 29 and ITU-T SG16. To the best of the authors' knowledge, the JVET work on the proposed SEI-based GFVC approach is the first standardization activity for generative video compression. The proposed SEI approach has not only advanced the reconstruction quality of early-day Model-Based Coding (MBC) via the state-of-the-art generative technique, but also established a new SEI definition for future GFVC applications and deployment. Experimental results illustrate that the proposed SEI-based GFVC approach can achieve remarkable rate-distortion performance compared with the latest Versatile Video Coding (VVC) standard, whilst also potentially enabling a wide variety of functionalities including user-specified animation/filtering and metaverse-related applications.