Horizontal gene transfer (HGT), or lateral gene transfer, is the non-sexual movement of genetic information between genomes. It has played a pronounced part in bacterial and archaeal evolution, but its role in eukaryotes is less clear. Behaviours unique to eukaryotic cells - phagocytosis and endosymbiosis - have been proposed to increase the frequency of HGT, but nuclear genomes encode fewer HGTs than bacteria and archaea. Here, I review the existing theory in the context of the growing body of data on HGT in eukaryotes, which suggests that any increased chance of acquiring new genes through phagocytosis and endosymbiosis is offset by a reduced need for these genes in eukaryotes, because selection in most eukaryotes operates on variation not readily generated by HGT.