The theory of relations has an eminent position in the classical set theory as well as in logic. Indeed, a relation is a basic object of the set theory that is used for many constructions (e.g. equality, ordering etc.) and a necessary step to define the concept of a function and thus, to develop mathematical analysis. The importance of relations has been proven in many other areas, for example in logic, relational databases or other areas of computer science. Not surprisingly, the theory of fuzzy relations possesses a similar position in the fuzzy set theory and consequently, in the related areas, such as fuzzy modelling, fuzzy relational databases etc. Considering a binary relation between elements from a universe X and elements from a universe Y, and a second binary relation between elements from Y and elements from Z, compositions are such mappings that gather the information hidden in both considered relations and map it into a newly created (composed) relation between elements from X and elements from Z, which is up to now unknown and potentially sought knowledge. And the way, how we construct the compositions, does influence the semantics of the composed relations as well as its application. Naturally, the same concepts may be defined in the fuzzy environment. In this talk, we will define the fundamental concepts of fuzzy relational compositions, explain the related semantics, introduce their properties and guide the students through distinct extensions and their applications.