In this talk, we introduce some recent progress on matrix weighted theory of the Fock projection. We show that the Muckenhoupt $A_p$-type condition characterizes the boundedness of the Fock projection on matrix weighted $L^p$-spaces. As applications, some function-theoretic and operator-theoretic properties for the vector-valued Fock spaces induced by matrix weights are established. This is based on joint works with Prof. Maofa Wang.