String Topology was introduced in 1999 by M. Chas and D. Sullivan, who defined a new algebraic structure, that of a BU-algebra, on the free loop space of a compact manifold. This structure describes interaction of strings (loops) in the manifold and mimics the Gromov-Witten invariants in a purely topological setting. I will discuss String Topology, as well as a higher-dimensional generalization of it, where strings get replaced by spheres. This generalization is related to Mochschild cohomology and a conjecture of Kontservich. Most part of this is joint work with Sullivan.