The floral structure of Alliaceae is assessed in relation to the systematics of the family, especially the nature of the component parts of the remarkably insect-like flower of Gilliesia graminea. Both presence of solid styles and possession of tenuinucellate ovules represent consistent synapomorphies for Alliaceae and support the separation of Agapanthus and Themidaceae from Alliaceae. Within Alliaceae, absence of septal nectaries (i.e., complete fusion of carpel margins) is a synapomorphy for the sister genera Gilliesia and Gethyum; septal nectaries are present in all other Alliaceae. A gynobasic style and reduced ovule number are probable synapomorphies for the genus Allium. In contrast to most other Alliaceae, in Gethyum and Gilliesia only three (abaxial) stamens (A1, a1, a2) are expressed, as in the apostasioid orchid Neuwiedia, but the perianth of Gethyum is only slightly bilaterally symmetric (zygomorphic), whereas Gilliesia graminea shows bilateral symmetry in all three floral whorls: perianth (suppression of the inner adaxial tepal in most flowers), androecium (suppression of three adaxial stamens), and gynoecium (slight bilateral symmetry, evident in transverse section). The precise relationships of Miersia and Solaria, the other two genera of Alliaceae with bilaterally symmetric flowers, are unknown, but their morphology indicates a close relationship with Gilliesia and Gethyum. Appendages of tepaline origin occur in Gethyum, Gilliesia, and Miersia; their papillate epidermis suggests that they function as osmophores. Their presence in Miersia, which has six stamens, indicates that these novel structures, which develop late in floral ontogeny, evolved independently from stamen suppression in this group. Within Gilliesia graminea, the genetic mechanisms controlling tepal number and shape are apparently unstable, resulting in fluctuating asymmetry. In G. graminea the possession of insect mimicry, presence of osmophores and absence of nectar together indicate a deceitful pollination mechanism similar to that of some Orchidaceae; this would make Gilliesia highly unusual among non-orchid monocots, given that pollination by sexual deceit is normally regarded as exclusive to orchids.