Reconfigurable intelligent surfaces (RISs) are an emerging technology for application to wireless networks. We introduce a physics and electromagnetic (EM) compliant communication model for analyzing and optimizing RIS-assisted wireless systems. The proposed model has four main notable attributes: (i) it is end-to-end , i.e., it is formulated in terms of an equivalent channel that yields a one-to-one mapping between the voltages fed into the ports of a transmitter and the voltages measured at the ports of a receiver; (ii) it is EM-compliant , i.e., it accounts for the generation and propagation of the EM fields; (iii) it is mutual coupling aware , i.e., it accounts for the mutual coupling among the sub-wavelength unit cells of the RIS; and (iv) it is unit cell aware , i.e., it accounts for the intertwinement between the amplitude and phase response of the unit cells of the RIS.