We all like and enjoy when a manifold or variety is symplectic. In algebraic geometry, a particularly interesting source of symplectic spaces comes in the form of moduli spaces of sheaves on K3 surfaces. There are other examples of spaces, such as moduli of sheaves on d-Calabi--Yau varieties or critical loci of functions, which cannot be symplectic in the classical sense but possess a "hidden" symplecticity. During the talk, I will introduce the notion of shifted symplectic structure and then discuss some examples and properties. In particular, we will see that the moduli of sheaves on a 3-Calabi--Yau variety is (-1)-symplectic and what this entails. Thanks to this fact, we will establish a bridge between the shifted symplectic world and enumerative geometry.