Operads are a general tool which allows one to encodetopological and algebraic structures and their relations.Recently, we defined an operad based on arcs on surfacesand showed that this operad (or rather its chains)has an explicit structure of a homotopy BV operad. The spaceon which this operad is defined is closely related toRiemann's moduli space and can be thought of a kind ofcombinatorial model for it. From this point of viewit is natural that the operad governs manytopological and algebraic questions, some of whichare related to physics.For instance, there is a suboperad of our operad,which is related to Chas-Sullivans' string topology.In this and other examples, we will show howthe natural composition of arcs in the arc operad yields thesestructures, gives them a surface interpretationand generalizes them.