Abstract: Self-similarity is defined, in a wide sense, as the property of some systems to be, either exactly or statistically, similar to a part of themselves. However, in the absence of an explicit embedding geometry, it is not clear how to decide what part of the system should be compared to (and look alike) the whole. In this sense, self-similarity is not an intrinsic property of the system but is directly related to the specific procedure to identify the appropriate subsystem. Scale invariance, on the other hand, implicitly assumes the existence of a metric space where the system is embedded, so that distance in this space gives a natural standard of measurement to uncover similar patterns at different observation scales. Despite many real complex networks are not explicitly embedded in any physical geometry, they can nevertheless be successfully embedded in hidden/effective metric spaces, which can then be used to define scale transformations in the spirit of the renormalization group. In this talk, I will explain how to uncover the self-similarity and scale-invariance of real complex networks. These properties have important implications (as well as applications) for the global structure of networks and the dynamics taking place on them.