In the optic of a more sustainable society, research and development of highly efficient fluid machines represent a fundamental process to satisfy the rapidly growing energy needs of the modern world. Radial turbines are characterized by higher efficiencies for a larger range of inflow conditions compared to axial turbines. Due to this favorable characteristic, they find their natural application in turbocharger systems, where the flow is inherently unsteady due to the engine reciprocating. In a turbocharged engine, to exploit the residual energy contained in the exhaust gases, the radial turbine is fed by the exhaust gases from the cylinders of the engine. The particular inflow conditions to which a turbocharger turbine is exposed, i.e. pulsating flow and high gas temperatures, make the turbocharger turbine a unique example in the turbomachinery field. Indeed, pulsating flow causes performance deviations from quasi-steady to pulsating flow conditions, while heat transfer deteriorates the turbine performance. Modeling correctly these phenomena is essential to enhance turbocharger-engine matching. The problem is further complicated since, due to the geometrical diversity of the different parts of the system, each component represents a stand-alone problem both in terms of flow characteristics and design optimization. In this thesis, high-fidelity numerical simulations are used to characterize the performance of a single-entry radial turbine applied in a commercial 4-cylinder engine for a passenger car under engine-like conditions. By treating the hot-side system as a stand-alone device, parametrization of the pulse shape imposed as inlet boundary conditions has let to highlight specific trends of the system response to pulse amplitude and frequency variations. Reduced-order models to predict the deviations of the turbine performance from quasi-steady to pulsating flow conditions are developed. At first, a simple algebraic model demonstrates the proportionality between the intensity of the deviations and the normalized reduced frequency. Then, a neural network model is demonstrated to accurately predict the unsteady turbine performance given a limited number of training data. Lastly, a gradient-based optimization method is developed to identify the optimum working conditions, in terms of pulse shape, to maximize the power output of the turbine. High-fidelity LES simulations are used to improve the understanding of flow physics. The flow at the rotor blade experiences different characteristics between continuous and pulsating flow conditions. In particular, large separations and secondary flows develop on both the pressure and suction sides of the blade as a consequence of the large range of relative inflow angles the blade is exposed to. Such secondary flows are addressed as the main cause of the drop of the isentropic efficiency from continuous to pulsating flow conditions.