Under certain conditions, the propagation of phonons in condensed matter systems and the propagation of light in general relativity are described by the same equation. However, while quantum phenomena like the emission of thermal radiation from black holes are hardly detectable, analogue systems can provide the unique possibility to experimentally test such effects. Originally driven by such motivation, the study of analogies between quantum field theory in curved space and condensed matter has now produced a fruitful interchange leading to new and deep insights in both fields. In particular Bose-Einstein Condesates are a very rich and powerful system in which this analogy can be implemented. I will give an overview on how various issues in the context of general relativity can be addressed through the analogy with BEC. Vice versa, techniques imported from general relativity can proficiently describe interesting phenomena in BEC, such as spontaneous phonon emission in flows crossing the speed of sound and resonant effects in system with multiple sonic points.