Genome-wide association studies have led to the development of polygenic score (PS) predictors that explain increasing proportions of the variance in human complex traits. In parallel, progress in preimplantation genetic testing now allows genome-wide genotyping of embryos generated via in vitro fertilization (IVF). Jointly, these developments suggest the possibility of screening embryos for polygenic traits such as height or cognitive function. There are clear ethical, legal, and societal concerns regarding such a procedure, but these cannot be properly discussed in the absence of data on the expected outcomes of screening. Here, we use theory, simulations, and real data to evaluate the potential gain of PS-based embryo selection, defined as the expected difference in trait value between the top-scoring embryo and an average, unselected embryo. We observe that the gain increases very slowly with the number of embryos, but more rapidly with increased variance explained by the PS. Given currently available polygenic predictors and typical IVF yields, the average gain due to selection would be ≈2.5cm if selecting for height, and ≈2.5 IQ (intelligence quotient) points if selecting for cognitive function. These mean values are accompanied by wide confidence intervals; in real data drawn from nuclear families with up to 20 offspring each, we observe that the offspring with the highest PS for height was the tallest only in 25% of the families. We discuss prospects and limitations of PS-based embryo selection for the foreseeable future.Polygenic scores (PS) are derived from large-scale genome-wide association studies (GWAS) of complex traits, which can be quantitative (such as intelligence or height) or categorical (such as disease status, in which case they are often referred to as 'polygenic risk scores') [8]. A PS is the count of effect alleles in an individual's genome, weighted by each allele's strength of association with the trait of interest in an independent GWAS [9]. The predictive power of a PS is usually represented by ps 2 , or the proportion of variance of the quantitative trait explained by the PS. To date, the largest GWAS of intelligence [10,11] has demonstrated a relatively modest out-of-sample ps 2 (≈5%), despite large sample sizes (n≈300,000 individuals). By contrast, recent large-scale GWASs of height have attained ps 2 of approximately 25%, while demonstrating a highly polygenic genetic architecture similar to intelligence [12]. Consequently, in the present report, we analyze height in addition to cognitive function, which also allows us to exploit several datasets in which height data, but not intelligence data, are available.PSs are typically evaluated on a cohort basis, and are not used to differentiate one individual from another (although a recent report has demonstrated that, for an extraordinarily tall NBA player, the PS for height was >4 standard deviations above the population mean [13]). In order for polygenic embryo selection to hold potential utility (independent of ethical considera...