Class-oriented techniques for reconstruction of dynamics from time series

•Reconstruction of dynamical systems from time series needs class-oriented techniques.•Reduction of the initial condition number is crucial for a hidden variable approach.•Methods for the recovery of delay times in time-delay systems are discussed.•Phase dynamics based methods are quite universal for studying coupled oscillators. Reconstruction of dynamical systems from time series is an important problem intensively studied within nonlinear dynamics and time series analysis for the last three decades. Its solution is a tool to accomplish prediction, classification, diagnostics and many other tasks. Universal approaches are quite attractive, but more specific techniques based on prior information about a system under study often appear advantageous in practice. We present an overview of the works of our team where such “class-oriented” techniques have been developed for realistic situations differing by the degree of prior knowledge: fully known structure of the dynamics equations with an accent to dealing with hidden variables and partly known structure for time-delay systems and coupled phase oscillators.