Lightning return-stroke models are needed for specifying the source in studying the production of transient optical emission (elves) in the lower ionosphere, the energetic radiation from lightning, and characterization of the Earth's electromagnetic environment, as well as studying lightning interaction with various objects and systems. Reviewed here are models based on Maxwell's equations and referred to as electromagnetic models. These models are relatively new and most rigorous of all models suitable for computing lightning electromagnetic fields. Maxwell's equations are numerically solved to yield the distribution of current along the lightning channel. Different numerical techniques, including the method of moments (MoM) and the finite difference time domain (FDTD) method, are employed. In order to achieve a desirable current-wave propagation speed (lower than the speed of light in air), the channel-representing wire is embedded in a dielectric (other than air) or loaded by additional distributed series inductance. Capacitive loading has been also suggested. The artificial dielectric medium is used only for finding the distribution of current along the lightning channel, after which the channel is allowed to radiate in air. Resistive loading is used to control current attenuation with height. In contrast with distributed circuit and so-called engineering models, electromagnetic return-stroke models allow a self-consistent full-wave solution for both lightning-current distribution and resultant electromagnetic fields. In this review, we discuss advantages and disadvantages of four return-stroke channel representations: a perfectly conducting/resistive wire in air, a wire embedded in a dielectric (other than air), a wire in air loaded by additional distributed series inductance, and a wire in air having additional distributed shunt capacitance. Further, we describe and compare different methods of excitation used in electromagnetic return-stroke models: closing a charged vertical wire at its bottom with a specified grounded circuit, a delta-gap electric field source, and a lumped current source. Finally, we review and compare representative numerical techniques used in electromagnetic modeling of the lightning return stroke: MoMs in the time and frequency domains and the FDTD method. We additionally consider the so-called hybrid model of the lightning return stroke that employs a combination of electromagnetic and circuit theories and compare this model to electromagnetic models.