Abstract: Derived representation schemes are an important concept in the study of non-commutative derived algebraic geometry. They are introduced by Berest et. al. and have found many applications and relations to fields such as noncommutative geometry, representation theory, homological algebra and many more. The derived representation schemes of Calabi-Yau algebras are even more interesting. In this talk I will introduce some basic concepts in this field, and discuss several examples and applications. Based on joint works with Berest, Eshmatov, Ramadoss and Yang.