Seshadri constants are measures of the local positivity of a line bundle on a projective variety. They were originally introduced by Demailly to attack the Fujita's conjecture. Although such attempt didn't work, Seshadri constants became a subject of intensive study in their own. In this talk, I will explain the definition of Seshadri constants and survey some of their applications to the arithmetic, symplectic and birational geometry of algebraic varieties.