Modern vehicle design relies on chassis control for increased performance and safety. These control strategies are realised through different actuators which target longitudinal, lateral dynamics, comfort or a combination of them. While classical and advanced control algorithms such as proportional-integral (PI), sliding mode control (SMC), model predictive control (MPC) have been extensively researched and utilized for vehicle chassis control, recent advances in artificial intelligence (AI) and computing have shown the potential of data-driven methods in performing a control task. This thesis aims to explore and analyse actor-critic deep reinforcement learning (DRL) for the design of control strategies for vehicle dynamics. In the context of this work the capabilities of DRL are analysed through two control strategies: torque vectoring (TV) and traction control (TC). Both control strategies are trained on high fidelity multibody vehicle simulation models created in AVL VSM that utilize nonlinear tyre models. The design and testing of the controllers also consider communication latencies, which is a well-known concern of reinforcement learning. The performance of DRL is compared against nonlinear model predictive control (NMPC) and SMC strategies using key performance indicators (KPI) over multiple test manoeuvres that highlight: i) the reference tracking capabilities, ii) control action smoothness and iii) safety indicators. Additionally, the low computational requirement of the trained DRL controllers is shown using real-time capable hardware. The collective results show DRL as a viable control strategy able to quantitatively outperform SMC and match the performance of high-fidelity model NMPCs. The complex internal models of the presented NMPCs make them non-real-time capable, which further highlights the performance per computational cost benefit of DRL. Furthermore, the DRL TV is trained in high tyre-road friction conditions, while the DRL TC is trained in various friction conditions. Once trained, both controllers are tested in different friction conditions, tyre and vehicle parameter changes with no further need to retune the controllers.