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Content Delivery Networks (CDNs) are Internet-scale systems that deliver streaming and web content to users from many geographically distributed edge data centers. Since large CDNs can comprise hundreds of thousands of servers deployed in thousands of global data centers, they can consume a large amount of energy for their operations and thus are responsible for large amounts of Green House Gas (GHG) emissions. As these networks scale to cope with increased demand for bandwidth-intensive content, their emissions are expected to rise further, making sustainable design and operation an important goal for the future. Since different geographic regions vary in the carbon intensity and cost of their electricity supply, in this paper, we consider spatial shifting as a key technique to jointly optimize the carbon emissions and energy costs of a CDN. We present two forms of shifting: spatial load shifting, which operates within the time scale of minutes, and VM capacity shifting, which operates at a coarse time scale of days or weeks. The proposed techniques jointly reduce carbon and electricity costs while considering the performance impact of increased request latency from such optimizations. Using real-world traces from a large CDN and carbon intensity and energy prices data from electric grids in different regions, we show that increasing the latency by 60ms can reduce carbon emissions by up to 35.5%, 78.6%, and 61.7% across the US, Europe, and worldwide, respectively. In addition, we show that capacity shifting can increase carbon savings by up to 61.2%. Finally, we analyze the benefits of spatial shifting and show that it increases carbon savings from added solar energy by 68% and 130% in the US and Europe, respectively.