This chapter offers a history of Preimplantation genetic diagnosis (PGD), an outline of each chapter, and a report on the European Society for Human Reproduction and Embryology (ESHRE) PGD Consortium. PGD was developed out of the need to provide an alternative to prenatal diagnosis for couples at risk of transmitting a genetic disease to their children. The challenge of introduction of molecular biology for PGD was the move from working with millions of cells to the very few cells of the embryo. Edwards and Hollands suggested that the method for single-cell diagnosis would be to use DNA probes for identifying the genotype of the human embryo and they predicted that high level of chromosome abnormalities would lead to complications in the interpretation of diagnostic tests. Methods used to study the chromosomes of gametes and embryos include karyotyping, Fluorescent in situ hybridization (FISH), metaphase-comparative genomic hybridization (CGH) and array-CGH.