This survey concerns the role of data structures for compactly storing and representing various types of information in a localized and distributed fashion. Traditional approaches to data representation are based on global data structures, which require access to the entire structure even if the sought information involves only a small and local set of entities. In contrast, localized data representation schemes are based on breaking the information into small local pieces, or labels , selected in a way that allows one to infer information regarding a small set of entities directly from their labels, without using any additional (global) information. The survey concentrates mainly on combinatorial and algorithmic techniques, such as adjacency and distance labeling schemes and interval schemes for routing, and covers complexity results on various applications, focusing on compact localized schemes for message routing in communication networks.