Access networks have been going through many reformations to make them adapt to arising traffic trends and become better suited for many new demanding applications. To that end, incorporating fog and edge computing has become a necessity for supporting many emerging applications as well as alleviating network congestions. At the same time, energy-efficiency has become a strong imperative for access networks to reduce both their operating costs and carbon footprint. In this dissertation, we address these two challenges in long-reach optical access networks. We first study the integration of fog and edge computing with optical access networks, which is believed to form a highly capable access network by combining the huge fiber capacity with closer-to-the-edge computing and storage resources. In our study, we examine the offloading performance under different cloudlet placements when the underlying bandwidth allocation is either centralized or decentralized. We combine between analytical modeling and simulation results in order to identify the different factors that affect the offloading performance within each paradigm. To address the energy efficiency requirement, we introduce novel enhancements and modifications to both allocation paradigms that aim to enhance their network performance while conserving energy. We consider this work to be one of the first to explore the integration of fog and edge computing with optical access networks from both bandwidth allocation and energy efficiency perspectives in order to identify which allocation paradigm would be able to meet the requirements of next-generation access networks.