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In recent years, the global use of online video services has increased rapidly. Today, a manifold of applications, such as video streaming, video conferencing, live broadcasting, and social networks, make use of this technology. A recent study found that the development and the success of these services had as a consequence that, nowadays, more than 1% of the global greenhouse-gas emissions are related to online video, with growth rates close to 10% per year. This article reviews the latest findings concerning energy consumption of online video from the system engineer's perspective, where the system engineer is the designer and operator of a typical online video service. We discuss all relevant energy sinks, highlight dependencies with quality-of-service variables as well as video properties, review energy consumption models for different devices from the literature, and aggregate these existing models into a global model for the overall energy consumption of a generic online video service. Analyzing this model and its implications, we find that end-user devices and video encoding have the largest potential for energy savings. Finally, we provide an overview of recent advances in energy efficiency improvement for video streaming and propose future research directions for energy-efficient video streaming services.