Over the past decades, network neuroscience has played a fundamental role in the understanding of large-scale brain connectivity architecture. Brains, and more generally nervous systems, can be modeled as sets of elements (neurons, assemblies, or cortical chunks) that dynamically interact through a highly structured and adaptive neurocircuitry. An interesting property of neural networks is that elements rich in connections are central to the network organization and tend to interconnect strongly with each other, forming so-called rich clubs. The ubiquity of rich-club organization across different species and scales of investigation suggests that this topology could be a distinctive feature of biological systems with information processing capabilities. This review surveys recent neuroimaging, computational, and cross-species comparative literature to offer an insight into the function and origin of rich-club architecture in nervous systems, discussing its relevance to human cognition and behavior, and vulnerability to brain disorders.