Two tests not to confuse
Preimplantation diagnosis looks for one known abnormality in a family at established risk. Aneuploidy screening counts the chromosomes of every embryo in a couple at no particular risk, to try to pick the best. They are different exercises, with different rules and very different levels of evidence.
Preimplantation diagnosis
It is tightly regulated: most legislations allow it only where the couple carry a high risk of transmitting a serious condition that is incurable at the time of diagnosis, and after review by a multidisciplinary panel. In practice: cystic fibrosis, spinal muscular atrophy, muscular dystrophy, Huntington's disease, haemoglobinopathies, or a chromosomal translocation causing recurrent miscarriage.
The process is an ICSI cycle — ICSI is required to avoid contamination by stray sperm — followed by a biopsy of a few trophectoderm cells at blastocyst stage, then vitrification while the result is awaited. Only unaffected embryos are transferred.
Aneuploidy screening
The idea is attractive: set aside embryos with the wrong number of chromosomes, which will not implant or will miscarry. Reality is more qualified. Randomised trials show no increase in the cumulative live birth rate per collection: the good embryo is transferred sooner, but no more of them are created. Then there is mosaicism — an embryo can hold both normal and abnormal cells, and healthy children have been born from embryos graded mosaic and discarded elsewhere. Some countries allow it, others forbid it.
If it is offered, two questions are worth asking: what benefit is expected in my situation, and what happens to embryos graded mosaic?
What the law allows almost nowhere
Sex selection for social reasons is prohibited in the great majority of countries, and admitted only to avoid an X-linked disease. Selection on non-medical traits — height, eye colour, predispositions — is allowed nowhere in Europe; the polygenic scores marketed elsewhere have no demonstrated predictive value at the level of one embryo.