In this paper, an overview of recent theoretical investigations and experimental characterization of the electromagnetic fields in the vicinity of a tower struck by lightning is presented. The presence of an elevated strike object has been included in two classes of return-stroke models, namely the engineering models and the electromagnetic or Antenna-Theory (AT) models. Extensions of engineering models based on distributed-source and lumped-source representations are described. The adequacy of the representation of the tall structure as an ideal uniform transmission line is discussed. Different approaches and assumptions for the computation of electromagnetic fields are summarized. Finally, recent progress in the characterization of electromagnetic fields radiated by lightning to tall structures is presented.