The last couple of years have witnessed the rapid development of prenatal molecular-based screening for fetal aneuploidies that utilizes the analysis of cell-free DNA circulating in the bloodstream of a pregnant woman. The present review looks at the potential and limitations of such testing and the possible causes of false-positive and false-negative results. The review also describes the underlying principles of data acquisition and analysis the testing involves. In addition, we talk about the opinions held by the expert community and some aspects of legislation on the use of noninvasive prenatal testing (NIPT) in clinical practice in the countries where NIPT is much more widespread than in Russia.