Preimplantation genetic diagnosis (PGD) aims to help couples with heritable genetic disorders to avoid the birth of diseased offspring or the recurrence of loss of conception. Following in vitro fertilization, one or a few cells are biopsied from each human preimplantation embryo for genetic testing, allowing diagnosis and selection of healthy embryos for uterine transfer. Although classical methods, including single-cell PCR and fluorescent in situ hybridization, enable PGD for many genetic disorders, they have limitations. They often require family-specific designs and can be labor intensive, resulting in long waiting lists. Furthermore, certain types of genetic anomalies are not easy to diagnose using these classical approaches, and healthy offspring carrying the parental mutant allele(s) can result. Recently, state-of-the-art methods for single-cell genomics have flourished, which may overcome the limitations associated with classical PGD, and these underpin the development of generic assays for PGD that enable selection of embryos not only for the familial genetic disorder in question, but also for various other genetic aberrations and traits at once. Here, we discuss the latest single-cell genomics methodologies based on DNA microarrays, single-nucleotide polymorphism arrays or next-generation sequence analysis. We focus on their strengths, their validation status, their weaknesses and the challenges for implementing them in PGD.