In this article, we describe the research area of evolving systems starting with a brief history, the basic concepts, and definitions and moving to classes of evolving systems. We further provide illustrative examples of evolving systems to various problems. The research area of evolving systems is closely related to adaptive systems, machine learning, mathematical modeling, data science, and computer systems. Some systems with such properties emerged at the end of last century, but the area was formed and recognized in the current century. The importance of this research – which is now a recognized niche topic with its own scientific journal (Evolving Systems), annualIEEEconferences, technical committees, etc. – is even clearer now when the era of Big Data, data streams, machine learning, and intelligence is a topic not only of research but also of publicity. The importance of evolving systems was stressed at the very beginning of its formation as a subdiscipline because a true intelligence can only be evolving. Indeed, the majority of the real processes and phenomena that people are interested in, such as modeling, predicting, classifying, controlling, or simply monitoring, are nonstationary; they are complex, nonlinear, and dynamically evolving. This includes climate, human behavior, social and biomedical systems, and even contemporary technical systems. The reality in which we are living now, couple of decades after the appearance of evolving systems, is characterized not only by a huge volume of exponentially growing data but also by their dynamically evolving nature, heterogeneous form, uncertainty, and often lack of structure. The classical theories and practical toolset (techniques, algorithms, and methods) have their own limitations and often rely on unrealistic assumptions. The concept of evolving systems was revolutionary and broke a number of these assumptions bringing the results closer to the reality of the problems, processes, and phenomena we study. One such key restrictive assumption usually made is about the fixed structure of the model of the system that describes processes or phenomena we are interested in. This is closely linked with the millennia old principle of approaching complex issues – “divide et Impera.” Adding to it “evolve” is vital.