AbstractPlanctomycetes, Verrucomicrobia and Chlamydia are prokaryotic phyla, sometimes grouped together as the PVC superphylum of eubacteria. Some PVC species possess interesting attributes, in particular, internal membranes that superficially resemble eukaryotic endomembranes. Some biologists now claim that PVC bacteria are nucleus‐bearing prokaryotes and are considered evolutionary intermediates in the transition from prokaryote to eukaryote. PVC prokaryotes do not possess a nucleus and are not intermediates in the prokaryote‐to‐eukaryote transition. Here we summarise the evidence that shows why all of the PVC traits that are currently cited as evidence for aspiring eukaryoticity are either analogous (the result of convergent evolution), not homologous, to eukaryotic traits; or else they are the result of horizontal gene transfers.