This paper presents an overview of the fundamentals of moving horizon state estimation and full information estimation. The paper provides a new statement of robust global asymptotic stability (RGAS) for state estimation and establishes a new result using this definition, namely that full information is RGAS for the case of a nonlinear detectable system subject to beta-convergent state and measurement disturbances. Two unsolved research problems are presented: (i) suboptimal moving horizon estimation and (ii) proving RGAS for the case of bounded rather than convergent disturbances. (c) 2012 Elsevier Ltd. All rights reserved.