Motivated by the increasing availability and quality of miniaturized sensors, computers, and wireless communication devices arid given their enormous potential, the use of wireless sensor networks (WSN) has become widespread. Because in many applications of WSNs one is required to estimate at each local sensor unit the state of a system given the measurements acquired by multiple sensors, there has been a flurry of activity related to the theory of distributed state estimation. This article contains a literature survey of distributed state estimation for discrete-time linear time invariant systems. In order to obtain the proper historical context, we review the state of the art in this field and summarize previous work. To provide the mathematical intuition behind some of the methods, this survey paper reproduces some of the main results given in the literature. It also provides a critical appraisal of the state of the art and affords the reader a comprehensive presentation of the most relevant results published so far. (C) 2019 Elsevier Ltd. All rights reserved.