System modelling and identification has played a key role in modern scientific research for system analysis, control and automation in many areas. This dissertation details the technical contributions of the applicant on parametric non linear system modelling and identification in the past 17 years since he joined Queen's University Belfast in 1998. The thesis first introduces the early research of the applicant on modelling the pollution emissions from fossil fuel fired thermal power plants for the purpose of reducing their negative environmental effects through advanced control. This work led to the proposal of a novel grey-box modelling approach for modelling complex system where many intermediate variables are difficult to measure on-line. Continual work has further led to the development of an algorithmic framework for building models that can be coined in a single hidden layer neural network structure with linear output weights . The first contribution along this stream of r~search is the proposal of a regression framework which allows the development of new fast algorithms to select a compact set of basis functions. This regression framework has further been extended for neural modelling with tunable parameters in the hidden nodes. In order to effectively optimize the two sets of parameters in 'the model and also to build a compact parsimonious model with less basis functions, hybrid approaches have been developed, which allow simultaneous selection of basis functions and optimization of the two sets of model parameters. These proposed methods and algorithms have been successfully applied to pollutant emission modelling in thermal power plants, soft-sensor development for measuring polymer melt viscosity in plastics industry, statistic process monitoring, as well as biological process modelling in systems biology, winning several prizes and awards. The research has further led to the development of new energy and condition monitoring systems currently used in the plastics industry