Modern problems of nonlinear dynamics arising in the context of dynamic chaos are investigated. Particular attention is paid to the synchronization of systems with chaotic dynamics - chaotic synchronization: its history, properties and prospects of applications. Considered are: problems of stability of chaotic synchronization in lattices of various geometric dimensions, composed of identical and non-identical dynamic systems (oscillators); tasks related to the development of dynamic chaos in systems with cylindrical phase space; problems of existence and stability of dynamic structures in lattices arising from self-organization of group (cluster) oscillators representing group synchronization subjects.