Designer babies are a currently hypothetical problem of the future; genetically modified human beings that parents tweak to be a bit better than the average human. As we inch ever closer to allowing gene therapy in sperm, eggs, and embryos, two views of the future are ever more frequently brought up for ethical hand-wringing.
One possibility is that genetic modification will allow for the elimination of diseases such as cystic fibrosis, Tay-Sachs, Huntington’s disease, neurofibromatosis, sickle cell disease, and quite literally hundreds of other diseases. And eliminate them not just from individual children, but from future generations -- a remedy that cures not only the individual, but also their children and their children's children, and so forth...
Also, though, you could make kids big, faster, smarter, stronger, and more beautiful (and also healthier, but in less important ways). While we might not trust parents to always make the best decisions for their children when it comes to rs7412-C, rs429358-T vs. rs7412-C, rs429358-C, the primary issue is that in early days this sort of treatment is likely to be limited by income. This raises the possibility of society becoming even more divided between the rich and the poor, perhaps even permanently, as some cynics have noted that the rich are not always willing to share their wealth and power.
We are probably still at least two generations from this becoming a serious socioeconomic issue, but we are at the point where we could be working on this right now, if we wanted -- and the upside of gene therapy is moving many scientists to think that we should be seriously pushing in this direction.