Organisms whose cells lack nuclei are called prokaryotic cells or prokaryotic organisms. They differ from organisms called eukaryotic, which have nuclei in most of their cells.
When cells first evolved, they did not possess nuclei or other organelles. These type of cells are bacteria. Bacteria are some of the most abundant organisms on the planet, and they have survived for billions of years without nuclei. While eukaryotic cells contain their genetic material inside the nucleus, bacteria allow their DNA to float freely in the cell. Some cells, such as human red blood cells, do not have a nucleus, even though most other cells in the organism do have them.