Modeling and control of port-Hamiltonian systems are extensively studied in the continuous-time literature as powerful tools for network modeling and control of complex physical systems. Since controllers are unavoidably implemented through digital devices, accurate sampled-data models and control strategies are highly recommended to prevent a negative impact on the closed-loop performances under digital control. This thesis contributes to the description of new port-Hamiltonian structures both in a purely discrete-time and sampled-data framework. Then, on these bases, stabilizing and energy-based digital feedback strategies are developed. Regarding modeling, the proposed state-space forms make use of the concepts of Difference/Differential Representation (DDR) of discrete-time dynamics and the discrete gradient function. The proposed models exhibit a Dirac structure that properly defines the storing, resistive and external elements of the concerned port-Hamiltonian system. For stabilization purposes, the u-average passivity property has been essential for properly discussing passivity-based-control (PBC) strategies such as damping output feedback and Interconnection and Damping Assignment (IDA-PBC) both in discrete time and under sampling. Three case studies from different physical domains aim to illustrate the computational aspects related to the modeling and control design and further we validate their performances by means of simulations.