Thanks to technological advances and environmental standards, as well as changing usage patterns, road vehicles are constantly developing. Electric and hybrid vehicles are playing an increasingly important role in today’s road transport. The most significant changes are probably in the powertrain of vehicles. The efficiency of internal combustion engines increases while their emissions continue to decline. In addition, high performance electric motors, batteries and even fuel cells play an increasingly important role in hybrid and electric vehicles. In this publication, we review the drive systems of current modern vehicles and the types and characteristics of their major components. We also review the available models and computer programs for their simulation, focusing mainly on MATLAB/Simulink applications. Based on this, we can develop our own models and simulation programs which will help us to perform different driving dynamics simulations and to compare the performance, dynamic and energetic characteristics of these powertrains and their components to each other.