Siphonophores are a group of pelagic colonial hydrozoans (Cnidaria) that have long been of general interest because of the division of labor between the polyps and medusae that make up these "superorganisms." These polyps and medusae are each homologous to free living animals but are generated by an incomplete asexual budding process that leaves them physiologically integrated. They are functionally specialized for different tasks and are precisely organized within each colony. The number of functional types of polyps and medusae varies across taxa, and different authors have used this character to construct phylogenies polarized in opposite directions, depending on whether they thought siphonophore evolution proceeded by a reduction or an increase in functional specialization. We have collected taxa across all major groups of siphonophores, many of which are found exclusively in the deep sea, using remotely operated underwater vehicles (ROVs) and by SCUBA diving from ships in the open ocean. We have used 52 siphonophores and four outgroup taxa to estimate the siphonophore phylogeny with molecular data from the nuclear small subunit ribosomal RNA gene (18S) and the mitochondrial large subunit ribosomal RNA gene (16S). Parsimony reconstructions indicate that functionally specialized polyps and medusae have been gained and lost across the phylogeny. Maximum likelihood and Bayesian analyses of morphological data suggest that the transition rate for decreased functional specialization is greater than the transition rate for increased functional specialization for three out of the four investigated categories of polyps and medusae. The present analysis also bears on several long-standing questions about siphonophore systematics. It indicates that the cystonects are sister to all other siphonophores, a group that we call the Codonophora. We also find that the Calycophorae are nested within the Physonectae, and that the Brachystelia, a historically recognized grouping of short-stemmed taxa, are polyphyletic. [Cnidaria; colonial animals; deep sea; division of labor; functional specialization; Hydrozoa; phylogenetics; Siphonophores.].