Abstract: This article reviews the theory and method of Green's functions in electromagnetism. The scalar Green's function associated with the scalar wave equation is first introduced, drawing an analogy to the impulse response function in signal systems. Subsequently, the dyadic Green's function for vector wave equations is presented, including Green's functions in both homogeneous and inhomogeneous media, and their connection with the reciprocity theorem and equivalence principle in electromagnetic theory. Lastly, the relation between Green's function theory with the motion effect of media and the quantum effect of electromagnetic fields is explored. Additionally, we discuss the applications of the electromagnetic Green's functions in engineering fields such as wireless communication and electromagnetic compatibility.