This is an overview paper that was written as a response to the discussion on the question: \textit{which of many systems of many-valued logics should be called fuzzy logic?} This question has been raised on the international conference ``The Logic of Soft Computing IV'', which took place in Ostrava, Czech Republic, in October 2005. The paper comments on the development and present state of fuzzy logic as a branch of mathematical logic. The paper briefly overviews the origin and motivation of fuzzy logic and then presents the main principles of t-norm based fuzzy logic both in its propositional as well as predicate form. Some further generalizations are also outlined.