the discovery that a huge number of everyday life systems share many common features and can thus be described through a unified theory. The remarkable diversity of these systems incorporates artificially or man-made technological networks such as the Internet and the World Wide Web (WWW), social networks such as social acquaintances or sexual contacts, biological networks of natural origin, such as the network of protein interactions of Yeast [1,3], and a rich variety of other systems, such as proximity of words in literature [4], items that are bought by the same people [5] or the way modules are connected to create a piece of software, among many others.The advances in our understanding of networks, combined with the increasing availability of many databases, allows us to analyze and gain deeper insight into the main characteristics of these complex systems. A large number of complex networks share the scale-free property [1,6], indicating the presence of few highly connected nodes (usually called hubs) and a large number of nodes with small degree. This feature alone has a great impact on the analysis of complex networks and has introduced a new way of understanding these systems. This property carries important implications in many everyday life problems, such as the way a disease spreads in communities of individuals, or the resilience and tolerance of networks under random and intentional attacks [7,8,9,10,11].Although the scale-free property holds an undisputed importance, it has been shown to not completely determine the global structure of networks [12]. In fact, two networks that obey the same distribution of the degrees may dramatically differ in other fundamental structural properties, such as in correlations between degrees or in the average distance between nodes. Another fundamental property, which is the focus of this article, is the presence of self-similarity or fractality. In simpler terms, we want to know whether a subsection of the network looks much the same as the whole [13,14,15,16]. In spite of the fact that in regular fractal objects the distinction between self-similarity and fractality is absent, in network theory we can distinguish the two terms: in a fractal network the number of boxes of a given size that are needed to completely cover the network scales with the box size as a power law, while a self-similar network is defined as a network whose degree distribution remains invariant under renormalization of the network (details on the renormalization process will be provided later). This essential result allows us to better understand the origin of important structural properties of networks such as the power-law degree distribution [17,18,19].