This thesis proposes a set of novel partition-based moving-horizon state estimation schemes for systems that are composed of interconnected and potentially geographically distributed subsystems, such as large-scale chemical plants or power system networks. To operate these systems in a safe and economically optimal manner, fast and accurate state estimates are crucial. The proposed methods provide such estimates by assigning dedicated estimators to each subsystem. In an iterative procedure, the estimators first solve a local optimization problem to compute an estimate of their subsystem's state, i.e., their partition of the overall system state, before communicating the results among each other. This partition-based approach avoids the dependence on a single, centralized computer, can benefit from parallel computation, and provides estimates of comparable accuracy to an optimal, centralized estimator. The thesis provides theoretical guarantees for the convergence and stability of the proposed estimators, analyses their behaviour under computational and communication constraints, and reports the results of their application to simulated chemical processes and power system networks.

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