As more and more complete bacterial and archaeal genome sequences become available, the role of lateral gene transfer (LGT) in shaping them becomes more and more clear. Over the long term, it may be the dominant force, affecting most genes in most prokaryotes. We review the history of LGT, suggesting reasons why its prevalence and impact were so long dismissed. We discuss various methods purporting to measure the extent of LGT, and evidence for and against the notion that there is a core of never-exchanged genes shared by all genomes, from which we can deduce the "true" organismal tree. We also consider evidence for, and implications of, LGT between prokaryotes and phagocytic eukaryotes.