De Rham cohomology of every complex smooth projective variety carries extra structure defined by a decomposition into holomorphic and anti-holomorphic parts called Hodge decomposition. In his groundbreaking papers Deligne introduced a notion of a mixed Hodge structure as a generalization of Hodge decomposition when a variety is not projective and smooth. Since then mixed Hodge structures obtained a lot of applications in the number theory, mirror symmetry, quantizations … I am going to give a gentle introduction to this beautiful work of Deligne and also discuss some classical application as well as the most recent one.