The explosive growth of mobile multimedia traffic calls for scalable wireless access with high quality of service and low energy cost. Motivated by the emerging energy harvesting communications, and the trend of caching multimedia contents at the access edge and user terminals, we propose a paradigm shifting framework, GreenDelivery, enabling efficient content delivery with energy harvesting based small cells. To resolve the two-dimensional randomness of energy harvesting and content request arrivals, proactive caching and push are jointly optimized, with respect to the content popularity distribution and battery states. We thus develop a novel way of understanding the interplay between content and energy over time and space. Case studies are provided to show the substantial reduction of macro BS activities, and thus the related energy consumption from the power grid is reduced. Research issues of the proposed GreenDelivery framework are also discussed.