Despite the sound theoretical, methodological, and experimental background inherited from 2D video, the stereoscopic video watermarking imposed itself as an open research topic. Paving the way towards practical deployment of such copyright protection mechanisms, the present paper is structured as a comparative study on the main classes of 2D watermarking methods (spread spectrum, side information, hybrid) and on their related optimal stereoscopic insertion domains (view or disparity based). The performances are evaluated in terms of transparency, robustness, and computational cost. First, the watermarked content transparency is assessed by both subjective protocols (according to ITU-R BT 500-12 and BT 1438 recommendations) and objective quality measures (five metrics based on differences between pixels and on correlation). Secondly, the robustness is objectively expressed by means of the watermark detection bit error rate against several classes of attacks, such as linear and nonlinear filtering, compression, and geometric transformations. Thirdly, the computational cost is estimated for each processing step involved in the watermarking chain. All the quantitative results are obtained out of processing two corpora of stereoscopic visual content: (1) the 3DLive corpus, summing up about 2 h of 3D TV content captured by French professionals, and (2) the MPEG 3D video reference corpus, composed of 17 min provided by both academic communities and industrials. It was thus established that for a fixed size of the mark, a hybrid watermark insertion performed into a new disparity map representation is the only solution jointly featuring imperceptibility (according to the subjective tests), robustness against the three classes of attacks, and nonprohibitive computational cost.