twisted calabi-yau algebras are a class of algebras with nice behavior regarding their hochschild cohomology. they include many classes of examples of recent interest, for example artin-schelter regular algebras. we discuss in particular the theory of twisted calabi-yau algebras of low global dimension which are factors of path algebras of quivers q. for example, we have preliminary results regarding the following question: for which quivers q does there exists a twisted calabi-yau algebra of dimension 3 which is a factor of the path algebra of q? for the pre-talk: we will give an introduction to some techniques from homological algebra, in particular hochschild cohomology, which are relevant for the talk.