Formation of a totipotent blastocyst capable of implantation is one of the first major milestones in early mammalian embryogenesis, but less than half of in vitro fertilized embryos from most mammals will progress to this stage of development. Whole chromosomal abnormalities, or aneuploidy, are key determinants of whether human embryos will arrest or reach the blastocyst stage. Depending on the type of chromosomal abnormality, however, certain embryos still form blastocysts and may be morphologically indistinguishable from chromosomally normal embryos. Despite the implementation of pre-implantation genetic screening and other advanced in vitro fertilization (IVF) techniques, the identification of aneuploid embryos remains complicated by high rates of mosaicism, atypical cell division, cellular fragmentation, sub-chromosomal instability, and micro-/multi-nucleation. Moreover, several of these processes occur in vivo following natural human conception, suggesting that they are not simply a consequence of culture conditions. Recent technological achievements in genetic, epigenetic, chromosomal, and non-invasive imaging have provided additional embryo assessment approaches, particularly at the single-cell level, and clinical trials investigating their efficacy are continuing to emerge. In this review, we summarize the potential mechanisms by which aneuploidy may arise, the various detection methods, and the technical advances (such as time-lapse imaging, “-omic” profiling, and next-generation sequencing) that have assisted in obtaining this data. We also discuss the possibility of aneuploidy resolution in embryos via various corrective mechanisms, including multi-polar divisions, fragment resorption, endoreduplication, and blastomere exclusion, and conclude by examining the potential implications of these findings for IVF success and human fecundity.