How are bacteria and archaea similar?
Both grow in a wide variety of habitats and conditions. Both have no nucleus, cytoskeleton or internal membranes.
The Domain Archaea wasn't recognized as a major domain of life until quite recently. Until the 20th century, most biologists considered all living things to be classifiable as either a plant or an animal. But in the 1950s and 1960s, most biologists came to the realization that this system failed to accomodate the fungi, protists, and bacteria.
The Archaea constitute a domain and kingdom of single-celled microorganisms. These microbes are prokaryotes, meaning they have no cell nucleus or any other membrane-bound organelles in their cells.