  This paper is a survey of our previous works on open-closed homotopy
algebras, together with geometrical background, especially in terms of
compactifications of configuration spaces (one of Fred's specialities) of
Riemann surfaces, structures on loop spaces, etc. We newly present Merkulov's
geometric A_infty-structure [Internat. Math. Res. Notices (1999) 153--164,
arxiv:math/0001007] as a special example of an OCHA. We also recall the
relation of open-closed homotopy algebras to various aspects of deformation
theory.
