These are tiny living cells which lack any organized membrane-bound structures within the cell. There is one chromosome in a circle and no membrane separates the chromosome from the rest of the cell. Formerly bacteria were the only members allocated to this group. They seem uncomplicated, but actually they have very fancy metabolic capabilities. And millions of different species have been identified mainly on the basis of their metabolisms.
Since the work of Carl Woese, this group of microbes has been divided into bacteria and archaea on the basis of one component of the ribosome (16SrRNA) which differs between the two groups. On this account, many now consider the term prokaryotes is irrelevant. The archaea look like bacteria but often live in much more hostile environments such as high salt content, high temperatures, high acidity etc. The two groups have biochemical features so different from each other that they are presumed to have entirely separate evolutionary histories.
Explaining how the gulf between the prokaryotes (bacteria and archaea) was crossed to bring about the eukaryotic cell, is a major problem for evolution theory. Many have considered it to be the “greatest single evolutionary discontinuity found in the present-day living world.” Although modern specialists tend not to focus their attention on this gap, it still constitutes a major problem about which one journalist joked: “How did one thing get inside another thing to form a complex thingamajig, and what were the things?” (Quamen p. 375) [David Quamen. The Tangled Tree. Simon & Schuster]
The bottom line in the origin of the eukaryotic cell from prokaryotes or their component bacteria and archaea, still has specialists squabbling about even basic issues like what the ancestral cell might have been like. The eukaryotic cell indeed clearly bears the marks of design! It certainly did not evolve.