Explore the application of the Multiscale Hybrid Mixed (MHM) method to polygonal meshes in this 50-minute lecture. Delve into the extension of the MHM method to polyhedral meshes, focusing on its hybrid formulation and static condensation for upscaling. Learn about the H(div)-conforming flux reconstruction and its implications for error estimation. Examine the Multiscale Hybrid (MH) method, a recent variant of MHM, and understand its key differences in Lagrange multiplier definition and problem formulation. Gain insights into collaborative research efforts in this field, including contributions from international institutions.