Research on corona discharge, shared by physics, chemistry and electrical engineering, has not arrested yet. As a dissipative process, the development of corona increases the resistive losses of transmission lines and enhances the line capacitance locally. Introducing additional losses and propagation delay, along the line, non-linearity and non-uniformity of the line parameters; therefore, corona should not be neglected. The present work is meant to provide the reader with comprehensive information on the corona macroscopic phenomenology and development, referring to the most relevant contributions in the literature on this subject. The models proposed in the literature for the simulation of the corona development are reviewed in detail, and sensitivity curves are provided to highlight their dependence on the input parameters.