There has recently been interest in the subject of homotopy representations emerging in Poisson Geometry. In this talk we explore the relations between homotopy representations of associative algebras and of Lie algebras in connection with the several algebraic structures that appear in the study of the Swiss-cheese operad. We refer to this class of algebraic structures as "Open-Closed Structures", which naturally include the OCHAs discovered by Kajiura and Stasheff.