The main aim of this PhD work is to advance tall-structure lightning return-stroke current modelling. The Alternative Transients Program (ATP), a version of the Electromagnetic Transients program (EMTP), is used to model the lightning current distribution within a tall structure and the attached lightning channel. The tall structure, namely the CN Tower, is modeled as three or five transmission line sections connected in series. The lightning channel is represented by a transmission line with a continuously expanding length. The presented model takes into account reflections within the tower and within the lightning channel. Locations of reflections, current reflection coefficients and the parameters of the current simulation function are calculated based on the time analysis of the current derivative signal, measured at the tower. The decay parameters of the simulation function are first determined by curve fitting the decaying part of the current obtained from measurement. The other parameters are determined by curve fitting the measured initial current derivative impulse with the derivative of the simulation function, before the arrival of reflections. The simulation results substantially succeeded in reproducing the fine structure of the measured current derivative signal. The model allows for the computation of the lightning current at any point along the current path (the tower and the attached channel), which is required for the calculation of the associated electromagnetic field. Using the three-section model of the tower, the presented return-stroke current model enables the determination of a discrete return-stroke velocity profile, demonstrating that the velocity generally decays with time. Furthermore, based on the five-section model, the proposed approach enables taking into account the existence of upward-connecting leaders, which allowed, for the first time, the determination of upward-connecting leader lengths and return-stroke velocity variation profiles with more details. The return-stroke velocity profile is found to initially increase rapidly with time, reaching a peak, and then decrease less rapidly. The proposed model is also experimentally verified based on the comparison between the computed and measured electromagnetic fields. The simulated electric and magnetic field waveforms are found to reproduce important details of the measured fields, including initial split peaks that appear due to channel-front reflections in the presence of upward-connecting leaders.