The realization that prokaryotes naturally and frequently disperse genes across steep taxonomic boundaries via lateral gene transfer gave wings to the idea that eukaryotes might do the same. Eukaryotes do acquire genes from mitochondria and plastids and they do transfer genes during the process of secondary endosymbiosis, the spread of plastids via eukaryotic algal endosymbionts. From those observations it, however, does not follow that eukaryotes transfer genes either in the same ways as prokaryotes do, or to a quantitatively similar degree. (...) An important illustration of the difference is that eukaryotes do not exhibit pangenomes, though prokaryotes do. Eukaryotes reveal no detectable cumulative effects of LGT, though prokaryotes do. A critical analysis suggests that something is deeply amiss with eukaryote LGT theories. In prokaryotes, genes from the environment can enter the genome via lateral gene transfer. In eukaryote genetics, natural variation comes from within the genome, not from the environment. Yet many reports claim that eukaryotes undergo LGT just like prokaryotes. Such claims do not withstand scrutiny and are probably untrue. (shrink)