Including energy harvesting capability in a wireless network is attractive for multiple reasons. First and foremost, powering base stations with renewable resources could significantly reduce their reliance on the traditional energy sources, thus helping in curtailing the carbon footprint. Second, including this capability in wireless devices may help in increasing their lifetime, which is especially critical for devices for which it may not be easy to charge or replace batteries. This will often be the case for a large fraction of sensors that will form the {em digital skin} of an Internet of Things (IoT) ecosystem. Motivated by these factors, this work studies fundamental performance limitations that appear due to the inherent unreliability of energy harvesting when it is used as a primary or secondary source of energy by different elements of the wireless network, such as mobile users, IoT sensors, and/or base stations. The first step taken towards this objective is studying the joint uplink and downlink coverage of radio-frequency (RF) powered cellular-based IoT. Modeling the locations of the IoT devices and the base stations (BSs) using two independent Poisson point processes (PPPs), the joint uplink/downlink coverage probability is derived. The resulting expressions characterize how different system parameters impact coverage performance. Both mathematical expressions and simulation results show how these system parameters should be tuned in order to achieve the performance of the regularly powered IoT (IoT devices are powered by regular batteries). The placement of RF-powered devices close to the RF sources, to harvest more energy, imposes some concerns on the security of the signals transmitted by these RF sources to their intended receivers. Studying this problem is the second step taken in this dissertation towards better understanding of energy harvesting wireless networks. While these secrecy concerns have been recently addressed for the point-to-point link, it received less attention for the more general networks with randomly located transmitters (RF sources) and RF-powered devices, which is the main contribution in the second part of this dissertation. In the last part of this dissertation, we study the stability of solar-powered cellular networks. We use tools from percolation theory to study percolation probability of energy-drained BSs. We study the effect of two system parameters on that metric, namely, the energy arrival rate and the user density. Our results show the existence of a critical value for the ratio of the energy arrival rate to the user density, above which the percolation probability is zero. The next step to further improve the accuracy of the stability analysis is to study the effect of correlation between the battery levels at neighboring BSs. We provide an initial study that captures this correlation. The main insight drawn from our analysis is the existence of an optimal overlapping coverage area for neighboring BSs to serve each other's users when they are energy-drained. / Ph. D. / Renewable energy is a strong potential candidate for powering wireless networks, in order to ensure green, environment-friendly, and self-perpetual wireless networks. In particular, renewable energy gains its importance when cellular coverage is required in off-grid areas where there is no stable resource of energy. In that case, it makes sense to use solar-powered base stations to provide cellular coverage. In fact, solar-powered base stations are deployed already in multiple locations around the globe. However, in order to extend this to a large scale deployment, many fundamental aspects of the performance of such networks needs to be studied. One of these aspects is the stability of solar-powered cellular networks. In this dissertation, we study the stability of such networks by applying probabilistic analysis that leads to a set of useful system-level insights. In particular, we show the existence of a critical value for the energy intensity, above which the system stability is ensured. Another type of wireless networks that will greatly benefit from renewable energy is internet of things (IoT). IoT devices usually require several orders of magnitude lower power compared to the base stations. In addition, they are expected to be massively deployed, often in hard-to-reach locations. This makes it impractical or at least cost inefficient to rely on replacing or recharging batteries in these devices. Among many possible resources of renewable energy, radio frequency (RF) energy harvesting is the strongest candidate for powering IoT devices, due to ubiquity of RF signals even at hard-to-reach places. However, relying on RF signals as the sole resource of energy may affect the overall reliability of the IoT. Hence, rigorous performance analysis of RF-powered IoT networks is required. In this dissertation, we study multiple aspects of the performance of such networks, using tools from probability theory and stochastic geometry. In particular, we provide concrete mathematical expressions that can be used to determine the performance drop resulting from using renewable energy as the sole source of power. One more aspect of the performance of RF-powered IoT is the secrecy of the RF signals used by the IoT devices to harvest energy. The placement of RF-powered devices close to the RF sources, to harvest more energy, imposes some concerns on the security of the signals transmitted by these RF sources to their intended receivers. We study the effect of using secrecy enhancing techniques by the RF sources on the amount of energy harvested by the RF-powered devices. We provide performance comparison of three popular secrecy-enhancing techniques. In particular, we study the scenarios under which each of these techniques outperforms the others in terms of secrecy performance and energy harvesting probability. This material is based upon work supported by the U.S. National Science Foundation (Grant CCF1464293). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the NSF.