Miscarriage affects approximately 15% of clinically recognized pregnancies, and 1–3% of couples experience pregnancy loss recurrently. Approximately 50–60% of miscarriages result from chromosomal abnormalities, whereas up to 60% of euploid recurrent abortions harbor variants in candidate genes. The growing number of detected genetic variants requires an investigation into their role in adverse pregnancy outcomes. Since placental defects are the main cause of first-trimester miscarriages, the purpose of this review is to provide a survey of state-of-the-art human in vitro trophoblast models that can be used for the functional assessment of specific abnormalities/variants implicated in pregnancy loss. Since 2018, when primary human trophoblast stem cells were first derived, there has been rapid growth in models of trophoblast lineage. It has been found that a proper balance between self-renewal and differentiation in trophoblast progenitors is crucial for the maintenance of pregnancy. Different responses to aneuploidy have been shown in human embryonic and extra-embryonic lineages. Stem cell-based models provide a powerful tool to explore the effect of a specific aneuploidy/variant on the fetus through placental development, which is important, from a clinical point of view, for deciding on the suitability of embryos for transfer after preimplantation genetic testing for aneuploidy.