I will discuss algebraic analogues of the string topology of Chas-Sullivan. I will talk about some older work of mine on Koszul duality and structures on higher Hochschild cohomology complexes of algebras over the k-dimensional little cubes operad. I will also talk about some new work I did on cactus sets and Batalin-Vilkovisky structure on the Hochschild cohomology of Poincare algebras.