This thesis investigates some problems on nonlinear system identification, parameter estimation, and signal processing. Random signal spectral analysis and system frequency response estimation are studied from incomplete time series. Both recursive and direct estimators are presented based on either an unbiased or minimum mean square error criterion. Nonlinear system identification and parameter estimation are studied. A quantisation technique is developed to give a clear geometrical interpretation for structure detection and parameter estimation. A new concept, state amplitude distance between current and previous operating states, is introduced, and results in a Variable Weighted Least Squares (VWLS) algorithm. A modified version makes on-line application possible. Jump resonance is predicted by the VWLS algorithm as one of the applications. Self-tuning controllers, including a nonlinear general predictive controller and a nonlinear deadbeat controller, are designed. A vector backward shift operator is defined to simplify the expression of the Hammerstein model, and is introduced to analyse the general feedback controller design problem for nonlinear plant described by the Hammerstein model. A fast root-solver developed facilitates nonlinear model treatment in on-line applications. Theoretical results are confirmed by simulation studies.