Clustering is commonly regarded as a synonym of unsupervised learning aimed at the discovery of structure in highly dimensional data. With the evident plethora of existing algorithms, the area offers an outstanding diversity of possible approaches along with their underlying features and potential applications. With the inclusion of fuzzy sets, fuzzy clustering became an integral component of Computational Intelligence (CI) and is now broadly exploited in fuzzy modeling, fuzzy control, pattern recognition, and exploratory data analysis. A lot of pursuits of CI are human-centric in the sense they are either initiated or driven by some domain knowledge or the results generated by the CI constructs are made easily interpretable. In this sense, to follow the tendency of human-centricity so profoundly visible in the CI domain, the very concept of fuzzy clustering needs to be carefully revisited. We propose a certain paradigm shift that brings us to the idea of knowledge-based clustering in which the development of information granules – fuzzy sets is governed by the use of data as well as domain knowledge supplied through an interaction with the developers, users and experts. In this study, we elaborate on the concepts and algorithms of knowledge-based clustering by considering the well known scheme of Fuzzy C-Means (FCM) and viewing it as an operational model using which a number of essential developments could be easily explained. The fundamental concepts discussed here involve clustering with domain knowledge articulated through partial supervision and proximity-based knowledge hints.