Lateral genetic transfer (LGT) is a major source of phenotypic innovation among bacteria. Determinants for antibiotic resistance and other adaptive traits can spread rapidly, particularly by conjugative plasmids, but also phages and natural transformation. Each successive step from the uptake of foreign DNA, its genetic recombination and regulatory integration, to its establishment in the host population presents differential barriers and opportunities. The emergence of successive multidrug-resistant strains of Staphylococcus aureus illustrates the ongoing role of LGT in the combinatorial assembly of pathogens. The dynamic interplay among hosts, vectors, DNA elements, combinations of genetic determinants and environments constructs communities of genetic exchange. These relations can be abstracted as a graph, within which an exchange community might correspond to a path, transitively closed set, clique or near-clique. We provide a set-based definition, and review the features of actual genetic exchange communities (GECs), adopting first a knowledge-driven approach based on literature, and then a synoptic data-centric bioinformatic approach. GECs are diverse, but share some common features.