There used to be 2 Domains in the classification system in taxonomy, Eukaryotes and one which included bacteria and Archea, now there are three, archea have been made a separate Domain.
The three domains, identified by Karl Woese, classify all living things into one of three large domains: Archaea (ar kay' uh), Bacteria, and Eukarya (yoo' kair ee' uh).
This was done based on Genetic relationships between the organisms concerned rather than that of Morphological similarities that the system was based upon in the past.
Scientists altered the classification of the domains when they were better able to define the genetic structures of living things. A new rDNA comparison analysis led to the development of the three domain system of classification.
It is to be noted that the new sector Archea are Prokaryote not Eukaryote, both Archea and Bacteria were joined before under the name Prokaryote, but now they have been separated.
The Eukarya domain contains all organisms with eukaryotic cells. From our classification system, then, the Eukarya domain would contain all members of kingdoms Protista, Fungi, Plantae, and Animalia.
The organisms that our system puts in kingdom Monera would go into either the Archaea domain or the Bacteria domain, depending on certain characteristics.
Those prokaryotic organisms that live in very extreme environments such as boiling hot springs or incredibly salty lakes belong in domain Archaea, while those prokaryotic organisms that live in more "normal" environments would belong in domain Bacteria.