Since 1989, the year of the first pre-implantation genetic diagnosis (PGD), many developments occurred both in assisted reproduction techniques and in molecular tools. While PGD is a well-established and documented application, pre-implantation genetic screening (PGS) for the detection of aneuploid embryos is still debated due to the presence of mosaicism in the embryo, but especially to the knowledge of the limits that label an embryo as healthy or as appropriate to the life. The aim of this review is to present the state-of-the-art in the field of PGD and PGS, illustrating its benefits and limitations, along with biopsy techniques and the use of new high-throughput technologies.