Non-invasive prenatal diagnosis of fetal chromosomal aneuploidies and monogenic diseases by analysing fetal DNA present in maternal plasma poses a challenging goal. In particular, the presence of background maternal DNA interferes with the analysis of fetal DNA. Using single molecule counting methods, including digital PCR and massively parallel sequencing, many of the former problems have been solved. Digital mutation dosage assessment can detect the number of mutant alleles a fetus has inherited from its parents for fetal monogenic disease diagnosis, and massively parallel plasma DNA sequencing enables the direct detection of fetal chromosomal aneuploidies from maternal plasma. The analytical power of these methods, namely sensitivity, specificity, accuracy and precision, should catalyse the eventual clinical use of non-invasive prenatal diagnosis.