Rapidly developing next-generation sequencing (NGS) technologies produce a large amount of data across the whole human genome and allow a large number of DNA samples to be analyzed simultaneously. Screening cell-free fetal DNA (cffDNA) obtained from maternal blood using NGS technologies has provided new opportunities for non-invasive prenatal diagnosis (NIPD) of fetal aneuploidies. One of the major challenges to the analysis of fetal abnormalities is the development of accurate and reliable algorithms capable of analyzing large numbers of short sequence reads. Several such algorithms have recently been developed. Here, we provide a review of recent NGS-based NIPD methods as well as the available algorithms for short-read sequence analysis. We furthermore introduce the practical application of these algorithms for the detection of different types of fetal aneuploidies, and compare the performance, cost and complexity of each approach for clinical deployment. Our review identifies several main technologies and trends in NGS-based NIPD. The main considerations for clinical development for NIPD and screening tests using DNA sequencing are: accuracy, intellectual property, cost and the ability to screen for a wide range of chromosomal abnormalities and genetic defects. The cost of the diagnostic test depends on the sequencing method, diagnostic algorithm and volume of the tests. If the cost of sequencing equipment and reagents remains at or around current levels, targeted approaches for sequencing-based aneuploidy testing and SNP-based methods are preferred.