One of the main challenges for mobile network operators today is the efficient delivery of mobile VoD services. In order to satisfy their requirements, we must revolutionize the way we manage the densely deployed resources in 5G wireless networks, and tailor their operation for video content delivery. Two key approaches that leverage the density of the 5G infrastructure are the systematic usage of in-network storage resources available in BSs for the deployment of smart caching policies, and the video delivery optimization techniques that leverage the novel multi-tier, dense, and heterogeneous structure of 5G systems. We first provide an overview of the main features of the densely deployed 5G networks that are expected to shape mobile VoD services. Next, we present specific solutions that have recently been proposed for each one of the approaches above, and discuss the main lessons learned. Finally, we discuss a number of open problems for video delivery in dense 5G systems.