Poisson structures appear naturally in many areas of mathematics. In 2005, Crawley-Boevey proposed the notion of an $H_{0}$-Poisson structure, which is a noncommutative generalization of Poisson structure. In this talk, we will focus on the higher homological extension of the $H_{0}$-Poisson structure: derived Poisson structure. In particular, we will talk about the relations between (cyclic) derived Poisson structures and derived moduli spaces parametrizing representations of associative algebras and Lie algebras. If time permits, I will talk about derived Poisson structure in string topology.