This monograph provides a sample of relevant new results on dynamical nonlinear statistical modeling and estimation which forms a basis for more effective signal processing, decision and control. While the research literature is rich in linear Gaussian methodologies, new contributions to the most relevant area of nonlinear and non-Gaussian processes have been scarce. Among the significant areas of application for which such methodologies are needed are: economics, biology, immunology, underwater acoustics, electric power generation, chemical process control, and variable structure systems in general. The latter include adaptive, intelligent, and decomposing mathematical structures or processes. The volume includes ten research papers on theory, computational methods, and applications. Topics include filtering with application to inertial navigation, structural-change detection, bilinear time-series models, bispectral estimation, threshold models, catastrophic models and a generalized eigenstructure method.