Thomas Cavalier-Smith states, "Eukaryotes and archaebacteria form the clade neomura and are sisters, as shown decisively by genes fragmented only in archaebacteria and by many sequence trees. This sisterhood refutes all theories that eukaryotes originated by merging an archaebacterium and an α-proteobacterium, which also fail to account for numerous features shared specifically by eukaryotes and actinobacteria."
When Carl Woese first published his three-domain system, it was believed that the domains Bacteria, Archaea, and Eukarya were equally old and equally related on the tree of life. However certain evidence began to suggest that Eukarya and Archaea were more closely related to each other than either was to Bacteria. This evidence included the common use of cholesterols and proteasomes, which are complex molecules not found in most bacteria. So, it was thought that there were two branches of life: Bacteria, and Neomura.
But recently, Cavalier-Smith showed evidence that Neomura evolved from Bacteria. The strongest evidence is that all known eukaryotes have mitochondria, which almost certainly evolved through endosymbiosis with an alpha-proteobacteria (a highly evolved group of bacteria). If Eukarya is as old as Bacteria, it almost certainly would have branched during the many millions of years it took for Bacteria to evolve the aerobic respiration performed by mitochondria, and some eukaryotes would have evolved without mitochondria.
A smaller but important piece of evidence is that the cholesterols and proteasomes found in Neomura are also found in Actinobacteria, perhaps the most highly evolved Bacteria. Molecules of this complexity are unlikely to evolve more than once in separate branches, so either there was a horizontal transfer of those two pathways, or Neomura evolved from this particular branch of the bacterial tree. This theory of Neomuran evolution is shown in the image to the right.