Fuzzy neural networks are connectionist systems that facilitate learning from data, reasoning over fuzzy rules, rule insertion, rule extraction, and rule adaptation. The concept of a particular class of fuzzy neural networks, called FuNNs, is further developed in this paper to a new concept of evolving neuro-fuzzy systems (EFuNNs), with respective algorithms for learning, aggregation, rule insertion, rule extraction. EFuNNs operate in an on-line mode and learn incrementally through locally tuned elements. They grow as data arrive, and regularly shrink through pruning of nodes, or through node aggregation. The aggregation procedure is functionally equivalent to knowledge abstraction. EFuNNs are several orders of magnitude faster than FuNNs and other traditional connectionist models. Their features are illustrated on a bench-mark data set. EFuNNs are suitable for fast learning of on-line incoming data (e.g., financial time series, biological process control), adaptive learning of speech and video data, incremental learning and knowledge discovery from large databases (e.g., in Bioinformatics), on-line tracing processes over time, life-long learning. The paper includes also a short review of the most common types of rules used in the knowledge-based neural networks.