Cellular data traffic almost doubles every year, greatly straining network capacity. The main driver for this development is wireless video. Traditional methods for capacity increase (like using more spectrum and increasing base station density) are very costly, and do not exploit the unique features of video, in particular a high degree of asynchronous content reuse. In this paper we give an overview of our work that proposed and detailed a new transmission paradigm exploiting content reuse, and the fact that storage is the fastest-increasing quantity in modern hardware. Our network structure uses caching in helper stations (femto-caching) and/or devices, combined with highly spectrally efficient short-range communications to deliver video files. For femto-caching, we develop optimum storage schemes and dynamic streaming policies that optimize video quality. For caching on devices, combined with device-to-device communications, we show that communications within clusters of mobile stations should be used; the cluster size can be adjusted to optimize the tradeoff between frequency reuse and the probability that a device finds a desired file cached by another device in the same cluster. We show that in many situations the network throughput increases linearly with the number of users, and that D2D communications also is superior in providing a better tradeoff between throughput and outage than traditional base-station centric systems. Simulation results with realistic numbers of users and channel conditions show that network throughput (possibly with outage constraints) can be increased by two orders of magnitude compared to conventional schemes.