This dissertation presents a study focused on exploring the integration of Dual-Clutch Transmissions (DCTs) in Hybrid Electric Vehicles (HEVs). Among the many aspects that could be investigated regarding the electrification of DCTs, research efforts are undertaken here to the development of control strategies for improving vehicle dynamic performance during gearshifts and the energy management of HEVs. In the first part of the dissertation, control algorithms for upshift and downshift maneuvers are developed for a Plug-in Hybrid Electric Vehicle (PHEV) architecture in which an electric machine is connected to the output of the transmission, thus obtaining torque filling capabilities during gearshifts. Promising results, in terms of the vehicle dynamic performance, are obtained for the two transmission systems analyzed: Hybrid Automated Manual Transmission (H-AMT) and Hybrid Dual-Clutch Transmission (H-DCT). On the other hand, the global optimal solution to the energy management problem for a PHEV equipped with a DCT is found by developing a detailed Dynamic Programing (DP) formulation. The main control objective is to reduce the fuel consumption during a driving mission. Based on the DP results, a novel real-time implementable Energy Management Strategy (EMS) is proposed. The performance of such controller, in terms of the overall fuel usage, is close to that of the optimal solution. Furthermore, the developed approach is shown to outperform a well-known causal strategy: Adaptive Equivalent Consumption Minimization Strategy (A-ECMS). One of the main aspects that differentiates the EMSs proposed here to those presented in previous works is the introduction of a model to estimate the energy consumption during gearshifts in DCTs. Thus, this dissertation illustrates how through the electrification of powertrains equipped with DCTs both the vehicle dynamic performance and the energy consumption can be improved.