Today video streaming has become the biggest contributor to Internet data traffic. With the ever increasing popularity of smart mobile devices for creating and consuming video content, in 5 years, mobile video content is predicted to account for over 78% of total mobile data traffic. This popularity of mobile devices for media consumption has resulted in a massive infrastructure deployment to support the growth. An adverse side effect of this growth is that IT industry is now a major contributor to total energy consumption in the world. On the other hand, users are struggling to manage the battery life of mobile devices as the battery technology on these devices has not kept pace despite the advancements in processing power, connectivity and sensing capabilities. This thesis introduces a novel energy efficient architecture for video streaming applications which factors into consideration the energy consumption of client devices as well as backend servers without negatively impacting the quality of experience of the end users. To this end, the conventional Quality of Experience (QoE) model in video streaming is augmented by incorporating energy status into the QoE model that has led the development of eDASH, an energy-aware dynamic adaptive streaming over HTTP, chunk selection algorithm for video streaming players. Furthermore, feasibility of utilising low-power servers to host and deliver video content is also investigated. Finally, this thesis proposes an energy efficient server management framework and content pre-caching algorithm for efficient utilisation of low-power servers in conjunction with eDASH clients.