Efficient usage of energy resources is a growing concern in today's communication systems. Solutions that consider energy harvesting (EH), where nodes in a communication system utilize other available energy sources, such as solar, wind power or man made signals, instead of completely relying on a fixed battery or the power from the grid, offer a promising perspective. EH capabilities not only enable efficient usage of energy sources but also offer enhanced mobility and prolonged network life-times. Hence communications systems powered by energy harvesting have a wide range of applications including environmental monitoring, process monitoring, smart homes and smart cities. Understanding the information transfer capabilities of communication systems under EH constraints is an important step for efficiently incorporating EH capabilities into our systems.This work addresses this problem within a framework that prioritizes practical low-complexity solutions. We have adopted an estimation theoretic perspective where the problem is investigated within a practical signal processing framework. We have focused on efficient transmission and resource allocation strategies. Practical receiver structures with linear filtering, low complexity designs such as linear precoders, power allocation methods were important ingredients in our work. Our resulting solutions complement the existing information theoretic solutions, and contribute to moving us one step closer to creating future green and smart communication systems.