The discovery of cell-free fetal (cff) DNA and RNA in the maternal circulation has driven developments in noninvasive prenatal diagnosis (NIPD) for the past decade. Detection of paternally derived alleles in cff DNA is becoming well established. Now much interest is focussing on NIPD of fetal chromosomal abnormalities, such as trisomy 21, which is a considerable challenge because this demands accurate quantitative measurements of the amounts of specific cff DNA or cff RNA sequences in maternal blood samples. Emerging strategies for distinguishing and quantifying the fetal nucleic acids in the maternal circulation promise continued development of the field, and pose a number of unanswered questions.