Video traffic has become a major part of mobile data traffic, and will keep growing in the coming years. The performance of video delivery is fundamentally constrained by the structure of the underlying wireless networks. The recently proposed heterogeneous cloud access networks have been widely recognized as an inevitable evolution trend of the current cellular system toward the future 5G system, where multiple hybrid radio access technologies coexist to provide flexible access for mobile users. As a key enabling functional block for high-performance video delivery, a powerful centralized baseband processing unit pool is adopted to control all the radio access technologies, and possibly facilitate the video encoding and transmission, which opens up the potential to achieve higher throughput, lower traffic delay, and greater robustness compared to its basic baseband processing unit counterpart without central control functions. However, such a centralized control framework also raises many new research challenges to be addressed. In this article, we provide an overview of the state-of-the-art video delivery architectures and video packet transmission strategies in heterogeneous cloud radio access networks, with highlights on the networking architectures, transmission strategies, performance analysis, and design challenges. This article also sheds some light on the design principles for future big-dataoriented wireless networks.