The discovery of circulating cell-free fetal nucleic acids in maternal plasma has opened up new possibilities for noninvasive prenatal diagnosis. The potential application of this technology for the noninvasive prenatal detection of fetal chromosomal aneuploidies is an aspect of this field that is being actively investigated. The main challenge of work in this area is the fact that cell-free fetal nucleic acids represent only a minor fraction of the total nucleic acids in maternal plasma. We performed a review of the literature, which revealed that investigators have applied methods based on the physical and molecular enrichment of fetal nucleic acid targets from maternal plasma. The former includes the use of size fractionation of plasma DNA and the use of the controversial formaldehyde treatment method. The latter has been achieved through the development of fetal epigenetic and fetal RNA markers. The aneuploidy status of the fetus has been explored through the use of allelic ratio analysis of plasma fetal epigenetic and RNA markers. Digital PCR has been shown to offer high precision for allelic ratio and relative chromosome dosage analyses. After a decade of work, the theoretical and practical feasibility of prenatal fetal chromosomal aneuploidy detection by plasma nucleic acid analysis has been demonstrated in studies using small sample sets. Larger scale independent studies will be needed to validate these initial observations. If these larger scale studies prove successful, it is expected that with further development of new fetal DNA/RNA markers and new analytical methods, molecular noninvasive prenatal diagnosis of the major chromosomal aneuploidies could become a routine practice in the near future.