This book is concerned with the variance-constrained optimized filtering problems and their potential applications for nonlinear time-varying dynamical systems. The distinguished features of this book are highlighted as follows.(1) A unified framework is provided for handling the variance-constrained filtering problems of nonlinear time-varying dynamical systems with incomplete information.(2) The application potentials of variance-constrained optimized filtering in networked time-varying dynamical systems are outlined. It contains some new concepts, new models and new methodologies with practical significance in control engineering and signal processing.It is a collection of several research results and thereby serves as a useful reference for upper undergraduate, postgraduate and engineers who are interested in studying (i) the variance-constrained filtering, (ii) recent advances affected by incomplete information and (iii) potential applications in practical engineering systems.