Scientists observe, discover, justify and eventually share their findings with the scientific community. Dissemination is an integral aspect of scientific discovery, since discoveries which go unnoticed have no or little impact on science. Today, peer review is part of this process of scientific dissemination as it contributes proactively to the quality of a scientific article. As the numbers of scientific journals and scientific articles published therein are increasing steadily, processes such as the single-blind or double-blind peer review are facing a near collapse situation. In fact, these traditional forms of reviewing have reached their limits and, because of this, are also increasingly considered as unfair, sloppy, superficial and even biased. In this manuscript, we propose forms of post-publication public peer review (P4R) as valuable alternatives to the traditional blind peer review system. We describe how the journal Sci has explored such an approach and provide first empirical evidence of the benefits and also challenges, such a P4R approach faces.