The thesis deals with modeling, experimental identification, and control system improvement of two characteristic vehicle powertrain components with emphasized friction effects: the tire on ice surface and the active differential wet clutch with electromechanical actuation system. The tire dynamics are considered in order to provide a physical explanation of observed effect of tire friction potential increase during an abrupt change of driving motor torque (dynamic tire friction potential, DTFP) and to investigate a possibility of the DTFP exploitation for the purpose of traction control system improvement. The active differential wet clutch research is aimed to gain insights into dynamic behavior of the overall clutch system, provide physical explanation of slow clutch torque response at low clutch relative speeds, and provide a basis for investigation of an advanced clutch control system. The presented methodology and results can also be applied to other vehicle elements such as brake or steering systems, dry clutches, railway vehicle wheels, and generally various mechatronic systems. A detailed analysis of the DTFP effect is given based on a comprehensive set of experimental results recorded by using an experimental electrical vehicle on slippery roads. It is shown that the influence of various operating parameters, such as the applied torque rise time or the vehicle speed, are actually a consequence of the characteristic tire rotation kinematics and the tire friction potential dependence on the dwell time of tire tread elements (so-called bristles). Based on these findings, the dynamic brush-type LuGre tire friction model has been extended with a distributed-parameter dynamic bristle dwell time model and an experimentally obtained dependence between the static friction potential and the bristle dwell time. The experimental validation results point out that the proposed model accurately describes the tire friction dynamics for a wide range of operating parameters. Finally, a concept of the traction control system is proposed and experimentally verified, which exploits the DTFP effect for the purpose of providing vehicle driving on an icy hill in the case when the static tire friction potential is lower than the up-hill driving resistive force. In the second part of the thesis, a multi-physical mathematical model of the active differential wet clutch is developed, which includes actuator dynamics (clutch normal force development dynamics), clutch torque development dynamics, thermal dynamics, and a multi-functional clutch friction coefficient model. Various approaches of friction elements modeling are analyzed and pragmatic model simplifications are proposed in order to increase the computational efficiency. The model parameters are obtained experimentally by using developed experimental setups. The model validation results point to a high level of modeling accuracy. The analysis of system responses shows that the actuator and the clutch friction effects have significant influence on the overall system dynamic response and that the traditional concept of clutch torque control based on actuator current control can be characterized by significant disadvantages. Using an experimentally obtained hysteresis-free dependence between the clutch normal force and the actuator motor position, a concept of clutch torque control based on actuator motor position closed-loop control is proposed, which shows a high static and dynamic control accuracy.