  The observed architecture of ecological and socio-economic networks differs
significantly from that of random networks. From a network science standpoint,
non-random structural patterns observed in real networks call for an
explanation of their emergence and an understanding of their potential systemic
consequences. This article focuses on one of these patterns: nestedness. Given
a network of interacting nodes, nestedness can be described as the tendency for
nodes to interact with subsets of the interaction partners of better-connected
nodes. Known since more than $80$ years in biogeography, nestedness has been
found in systems as diverse as ecological mutualistic organizations, world
trade, inter-organizational relations, among many others. This review article
focuses on three main pillars: the existing methodologies to observe nestedness
in networks; the main theoretical mechanisms conceived to explain the emergence
of nestedness in ecological and socio-economic networks; the implications of a
nested topology of interactions for the stability and feasibility of a given
interacting system. We survey results from variegated disciplines, including
statistical physics, graph theory, ecology, and theoretical economics.
Nestedness was found to emerge both in bipartite networks and, more recently,
in unipartite ones; this review is the first comprehensive attempt to unify
both streams of studies, usually disconnected from each other. We believe that
the truly interdisciplinary endeavour -- while rooted in a complex systems
perspective -- may inspire new models and algorithms whose realm of application
will undoubtedly transcend disciplinary boundaries.
