An exposition of the results on synchronization and state estimation of nonlinear systems over the limitedband communication channel is given. Relevance of passifiability condition for controlled synchronization of master-slave nonlinear systems for first order and full-order coder/decoder pairs is demonstrated. The algorithm for state estimation of spatially distributed systems based on the local measurements and quantization of the transmitted data is developed, and its limit opportunities are studied. The numerical and experimental results for various physical systems are described, demonstrating practical applicability of the theoretical statements and high efficiency of the proposed estimation and synchronization schemes.