The present invention relates to methods of enriching fetal cells from a pregnant female. The present invention relates to removing, from a sample, cells that comprise at least one MHC molecule. The present invention also relates to methods that rely on using telomerase, mRNA encoding components thereof, as well as telomere length, as markers for fetal cells. Enriched fetal cells can be used in a variety of procedures including, detection of a trait of interest such as a disease trait, or a genetic predisposition thereto, gender typing and parentage testing.