In the recent years, the saturation of the smartphone market penetration fostered the development of new applications to connect human beings with smart objects. However, the explosive growth in the number of connected devices brings some concerns about the highly growing traffic and the environmental effect of batteries production and disposal. Simultaneous wireless information and power transfer (SWIPT) technique has been emerged as a solution to mitigate with these concerns. However, SWIPT also comes with some obstacles such as the limitations on the energy transfer efficiency due to the propagation losses and the constraints on the minimum received power imposed by the current radio frequency (RF) harvesting technologies. This restricts the range of application of wirelessly powered devices by limiting them to the execution of very simple computational tasks. Following this line of thought, the integration of SWIPT with mobile edge computing (MEC) has appeared as an enticing emerging research direction to increase the computational capabilities of SWIPT enabled systems. This dissertation focuses on studying the performance of SWIPT enabled MEC system in the presence of spatially correlated shadowing. The first step taken towards this objective is the analysis of the performance of SWIPT enabled systems with special emphasis on the impact of spatially correlated shadowing on the achievable rate-energy trade-off. Stochastic geometry is used to model the random location of the network nodes and the geometry of the propagation environment. Capitalizing on the analytical tool developed in the first part of the dissertation, the analysis of the achievable performance trade-offs has been extended to SWIPT-enabled computing systems. The last part of the dissertation addresses the study of SWIPT-MEC systems and provides an analytical tool to compute the probability of successfully execute a task as a function of the network parameters. The last chapter is devoted to a comprehensive study of SWIPT-enabled MEC systems in the presence of spatially correlated shadowing at a network level. (FSA - Sciences de l'ingénieur) -- UCL, 2022