Social media poses three major challenges, dubbed by Gartner the 3Vs of big data: volume, velocity, and variety. This research contribution presentation will present deep data and content analytics methods to address the fourth crucial, but hitherto largely unstudied, big data challenge: veracity. Novel cross-disciplinary social semantic methods for computing veracity from the PHEME European project will be presented. PHEME combines document semantics, a priori large-scale world knowledge (Linked Open Data) and a posteriori knowledge and context from social networks, cross-media links and spatio-temporal metadata. Key novel contributions are dealing with multilinguality, modelling rumour dynamics over time, contradiction and misinformation detection, and longitudinal models of users, influence, and trust.