A review is given on an extended form of Maxwell's equations which is based on Lorentz invariance in combination with a nonzero divergence of the electric field E in vacuo. In addition to the displacement current, this form includes a “space-charge current” 0 (div E)C where the modulus of C is equal to the velocity c of light and the direction of C depends on the particular geometry. This form predicts new states to exist, such as steady equilibria and additional types of wave phenomena. Among the equilibria there are axisymmetric “particle-shaped” and “string-shaped” states. The former result in one class of solutions with nonzero integrated charge q0, magnetic moment M0, mass m0, and angular momentum s0, and in another class with vanishing q0 and M0 but nonzero m0 and s0. These solutions could contribute to the understanding of charged and neutral leptons. The latter states can be of interest to the string model of the hadron structure. Among the new wave types there are plane and axisymmetric modes. The former provide a possible solution to the problem of total reflection at the interface between a dissipative medium and vacuum. The latter types provide a model of the individual photon as a boson wave packet with an angular momentum, a nonzero but small rest mass. and a radius being in agreement with microwave experiments.