Distributed state estimation is of paramount importance in many applications involving the large-scale complex systems over spatially deployed networked sensors. This paper provides an overview for analysis of distributed state estimation algorithms for linear time invariant systems. A number of previous works are reviewed and a clear classification of the main approaches in this field are presented, i.e., Kalman-filter-type methods and Luenberger-observer-type methods. The design and the stability analysis of these methods are discussed. Moreover, a comprehensive comparison of the existing results is provided in terms of some standard metrics including the graph connectivity, system observability, optimality, time scale and so on. Finally, several important and challenging future research directions are discussed.