This dissertation deals with research on the numerical modelling of electrical discharges in laboratory long air gaps excited with positive switching impulses. It begins with the preliminary work of several scientists during the last decades, making a detailed analysis of different approaches for modelling all the stages in a full discharge. The relations between these models are identified as well as the effect on the outcome when modifying some important input parameters. The general concept describing the discharge phenomenon usually includes three main elements: the streamer inception, the streamer-to-leader transition and the stable leader propagation. These elements are present in many of the analysed models and the main differences between them are the assumptions and simplifications made by each author at a specific point in their methodologies. The models are usually simplified by assigning experimentally determined values to physical constants pertinent to different stages of the full discharge. These constants are the potential gradient in the leader-corona region to sustain the leader propagation, the charge per unit length along the leader channel which depends on the atmospheric conditions and the voltage impulse wave shape; and the leader propagation velocity, which is closely related to the discharge current. The dissertation includes the results of laboratory work related the study of leaders in long gap discharges, electrical parameters and optical records. By reconstructing the three-dimensional leader propagation for the rod-to-plane configuration, it was possible to study the random tortuous path followed by the leader as it propagates. One important element included in the discharge modelling is the representation of the leader-corona region in front of the leader tip as it propagates towards the grounded electrode. For the calculation of the net charge available in the leader-corona region, two new methodologies were pro-posed based on the electrostatic potential distribution obtained from a finite element method solver. This allowed the inclusion of more elements representing different parts of the discharge in the simulation domain. In the final part, all the analysed elements and the new proposed ones were included in a new methodology for the modelling of electrical dis-charges in long air laboratory gaps. The results obtained from this methodology were compared to experimental data. A good agreement was found between the simulation results and the experimental data.