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.