Power systems, traffic and communication networks, irrigation systems, hydropower valleys, or smart grids are composed of structured interconnections of lower-dimensional subsystems. To monitor such systems, one has to know the values of the variables in the system. Since in general not all these variables can be measured, they must be estimated, based on the system model and available measurements. However, there is no general method to design estimators for nonlinear systems. The challenge of designing an estimator becomes even more difficult if the system is distributed.