A precise understanding of the radio emission from extensive air showers is of fundamental importance for the design of cosmic ray radio detectors as well as the analysis and interpretation of their data. In recent years, tremendous progress has been made in the understanding of the emission physics both in macroscopic and microscopic frameworks. A consistent picture has emerged: the emission stems mainly from time-varying transverse currents and a time-varying charge excess; in addition, Cherenkov-like compression of the emission due to the refractive index gradient in the atmosphere can lead to time-compression of the emitted pulses and thus high-frequency contributions in the signal. In this article, I discuss the evolution of the modelling in recent years, present the emission physics as it is understood today, and conclude with a description and comparison of the models currently being actively developed.
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