Efficient video compression algorithms in advanced multimedia broadcasting systems are in high demand. In the last decades, different video compression tools have been developed which can influence the final Quality of Experience in different ways. his paper has two goals. The first goal is to present a study of different compression algorithms available for stereoscopic 3D videos. The second goal is to present the possibilities in the creation of new stereoscopic models. The well-established video codecs (AVC, MVC, HEVC and MV-HEVC) are considered as encoders. Generic objective video quality metrics are used to analyze the compression efficiencies of the considered codecs, extended with results from subjective tests. The correlations between the objective and subjective scores are analyzed statistically. Due to unsatisfactory results of generic 2D metrics for the stereoscopic sequences used in the test, new objective models are presented. Such models show improved correlation with subjective stereoscopic video quality. The validation, verification and a description of models are presented in detail.