Observer design is an essential part of many controller design algorithms because in many applications, measured information alone does not sufficiently represent the system's state. In particular, estimating the system's state can be done by multiple observers cooperatively, which is referred to as distributed estimation. The essential benefit lies in the fact that through cooperation, each individual observer only needs very limited sensor capacity, which allows for large, spatially distributed sensor networks. This thesis is dedicated at improving distributed estimation in a number of ways, including - extending the system class towards nonlinear systems - implementing event-triggered communication - enabling decentralized computation of the observer parameters - preserving scalability of the estimation scheme for systems of increasing size Moreover, we apply such cooperating observers to solving the synchronization and output regulation problem for multi-agent systems.