This paper aims to consolidate the work carried out in making base station (BS) green and energy efficient by integrating renewable energy sources (RES). Clean and green technologies are mandatory for reduction of carbon footprint in future cellular networks. RES, especially solar and wind, are emerging as a viable alternate to fossil fuel based energy, which is the main cause of climate pollution. With advances in technologies, renewable energy is making inroads into all sectors including information and communication technologies (ICT). The main contributors of energy consumption in ICT sector are ’data centers' and ’cellular networks'. In cellular networks the BS is the main consumer of energy, mostly powered by the utility and a diesel generator. This energy comes at a significant operating cost as well as the environmental cost in terms of harmful greenhouse gas (GHG) emissions. Recent research shows that powering BSs with renewable energy is technically feasible. Although installation cost of energy from non-renewable fuel is still lower than RES, optimized use of the two sources can yield the best results. This paper presents a comprehensive overview of resource management in cellular BSs powered by RES and an in-depth analysis of power consumption optimization in order to reduce both cost and GHGs. Renewable energy sources are not only feasible for a stand-alone or off-grid BSs, but also feasible for on-grid BSs. This paper covers different aspects of optimization in cellular networks to provide reader with a holistic view of concepts, directions, and advancements in renewable energy based systems incorporated in cellular communications. Energy management strategies are studied in the realm of smart grids and other technologies, increasing the possibilities for energy efficiency further by employing schemes such as ‘energy cooperation’. Finally, the paper supports the move towards green communication in order to contribute positively towards climate change.