The concept of well quasi-order is a generalization of the classical notion of well order and plays a role in the studying of several problems of Mathematics and Theoretical Computer Science. This paper concerns some applications of well quasi-orders to Formal Language Theory. In particular, we present a survey of classical and recent results, based upon such structures, concerning context-free and regular languages. We also focus our attention to some application of well quasi-orders in the studying of languages obtained by using the operators of shuffle and iterated shuffle of finite languages.