A general framework and a holistic concept are proposed in this paper that combine computationally light machine learning from streaming data with the online identification and adaptation of dynamic systems in regard to their structure and parameters. According to this concept, the system is assumed to be decomposable into a set of fuzzily connected simple local models. The main thrust of this paper is in the development of an original approach for the self-design, self-monitoring, self-management, and self-learning of such systems in a dynamic manner from data streams which automatically detect and react to the shift in the data distribution by evolving the system structure. Novelties of this contribution lie in the following: 1) the computationally simple approach (simpl_e_Clustering-simplified evolving Clustering) to data space partitioning by recursive evolving clustering based on the relative position of the new data sample to the mean of the overall data, 2) the learning technique for online structure evolution as a reaction to the shift in the data distribution, 3) the method for online system structure simplification based on utility and inputs/feature selection, and 4) the novel graphical illustration of the spatiotemporal evolution of the data stream. The application domain for this computationally efficient technique ranges from clustering, modeling, prognostics, classification, and time-series prediction to pattern recognition, image segmentation, vector quantization, etc., to more general problems in various application areas, e. g., intelligent sensors, mobile robotics, advanced manufacturing processes, etc.