Let $G$ be a real classical group of type $B$, $C$, $D$ (including the real metaplectic group). We consider a nilpotent adjoint orbit $check{mathcal O}$ of $check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We classify all special unipotent representations of $G$ attached to $check{mathcal O}$, in the sense of Barbasch and Vogan. When $check{mathcal O}$ is of good parity, we construct all such representations of $G$ via the method of theta lifting. As a consequence of the construction and the classification, we conclude that all special unipotent representations of $G$ are unitarizable, as predicted by the Arthur-Barbasch-Vogan conjecture. We also determine precise structure of the associated cycles of special unipotent representations of $G$.
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