Many constructions such as taking the critical locus of a functional or taking a quotient by symmetries are needed in physics. On the other hand, derived geometry is motivated by the need to perform operations such as non-transversal intersections or quotients on generalised geometric spaces. In this talk, I will first speak of (shifted) symplectic geometry in the context of derived geometry. I will then describe how to construct new symplectic structures from old ones (in particular on derived critical loci) that will recover and generalise constructions such as the symplectic reduction or the AKSZ formalism.