It is a well known fact that nowadays we are faced with not only large data sets that we need to process quickly, but with huge data streams (Domingos and Hulten, 2001). Special requirements are also placed by the fast growing sector of autonomous systems where systems that can re-train and adapt ‘on-fly’ are required (Patchett and Sastri, 2007). Similar requirements are enforced by the advanced process industries for self-developing and self-maintaining sensors (Qin et al., 1997). Now they even talk about self-learning industries (EC, 2007). All of these requirements cannot be met by using off-line methods and systems that can only adjust their parameters and/or are linear (Astroem and Wittenmark, 1989). These requirements call for a new type of systems that assumes the structure of non-linear, non-stationary systems to be adaptive and flexible. The author of this chapter started research work in this direction around the turn of the century (Angelov and Buswell, 2001; Angelov, 2002) and this research culminated in proposing with Dr. D. Filev the so called evolving Takagi-Sugeno (eTS) fuzzy system (Angelov and Filev, 2003). Since then a number of improvements of the original algorithm has been done, which require a systematic description in one publication. In this chapter an enhanced version of the eTS algorithm will be described which is called eTS+. It has been tested on a data stream from real engine test bench (data provided courtesy of Dr. E. Lughofer, Linz, Austria). The results demonstrate the superiority of the proposed enhanced approach for modeling real data stream in precision, simplicity and interpretability, and computational resources used. (c) IEEE Press and John Wiley and Sons