Social media have emerged in the last decade as a viable and ubiquitous means of communication. The ease of user content generation within these platforms, e.g. check-in information, multimedia data, etc., along with the proliferation of Global Positioning System (GPS)-enabled, always-connected capture devices lead to data streams of unprecedented amount and a radical change in information sharing. Social data streams raise a variety of practical challenges, including derivation of real-time meaningful insights from effectively gathered social information, as well as a paradigm shift for content distribution with the leverage of contextual data associated with user preferences, geographical characteristics and devices in general. In this article we present a comprehensive survey that outlines the state-of-the-art situation and organizes challenges concerning social media streams and the infrastructure of the data centres supporting the efficient access to data streams in terms of content distribution, data diffusion, data replication, energy efficiency and network infrastructure. We systematize the existing literature and proceed to identify and analyse the main research points and industrial efforts in the area as far as modelling, simulation and performance evaluation are concerned.