Here's some stuff that would cause a problem is they happened, but that I don't think will happen:
Mind body transfer
People living forever
Artificial wombs
Here's some that might happen:
Prenatal genetic selection, or alteration
Human cloning
Very expensive treatments that can not be afforded by many
Having children very late in life (i.e. within
a decade or two of expected death)
I don't know if it's possible to get it, but try to watch the show Century City, or at least read episode synopses. Your question is the premise of the show.