In our real life problems many ambiguities and uncertainties exist. So it is difficult to express such problems in terms of classical set theory which only considers two phases ‘belongs to’ and ‘not belongs to’. So classical set theory is unable to capture such uncertainties. In \(1965\) , Lotfi Asker Zadeh first introduced the notion of a fuzzy set. The fuzzy set is able to capture uncertainties in our real-life problems. Later many extensions of fuzzy sets are introduced. The natural question arises about the motivation and relations among all the extensions of fuzzy sets. In this study, the fuzzy set and its extensions such as type- \(2\) fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set, bipolar fuzzy set, neutrosophic fuzzy set, picture fuzzy set, rough set, and soft set are discussed. This study reviews recent developments of fuzzy sets and analyses their relations. Also, the motivation and application areas of all such extensions are studied here.