This dissertation focuses on the study of spin-lattice and magnon-phonon coupling in multiferroic materials based on their electrodynamic response. Based on a study of the electrodynamic response in the far infrared region of the electromagnetic spectrum of 2 families of multiferroic compounds, a new elementary excitation has been discovered, called electromagnon. This is the central topic of this thesis. The electromagnon is a hybrid excitation composed of phonon and magnon parts that is observable in these materials due to to its electric dipole coupling to the electromagnetic field. This coupling comes about due to the strong magnetoelectric interactions in these materials that are responsible for their multiferroic behavior. Models that describe the experimental features of these excitations are outlined for each of these families of multiferroics.