  We generalize an important class of Banach spaces, namely the $M$-embedded
Banach spaces, to the non-commutative setting of operator spaces. The one-sided
$M$-embedded operator spaces are the operator spaces which are one-sided
$M$-ideals in their second dual. We show that several properties from the
classical setting, like the stability under taking subspaces and quotients,
unique extension property, Radon Nikod$\acute {\rm{y}}$m Property and many
more, are retained in the non-commutative setting. We also discuss the dual
setting of one-sided $L$-embedded operator spaces.
