Every operator space sits inside its second dual via a canonical complete isometric embedding. We say, X is one-sided M-embedded if X is a one-sided M-ideal in X**. There is a vast classical theory of such spaces for the Banach spaces. They behave well with respect to subspaces and quotients, and have many properties like unique extension property, approximation property of the dual to name a few. We show that many of the classical results generalize to operator spaces and a lot of these nice properties are also retained.