Few organisms like some bacteria and yeasts can respire without air. They undergo anaerobic respiration. It is a type of respiration that takes place in the cytoplasm of the cell and involves the partial breakdown of glucose. This kind of respiration releases low energy as compared to the aerobic respiration that takes place in the presence of oxygen and takes place in the cytoplasm as well as the mitochondria.
The organisms that undergo this type of respiration are known as anaerobes. They can be facultative anaerobes i.e they usually undergo aerobic respiration but when the oxygen is absent they'll take up the anaerobic pathway, or the obligate anaerobes that always undergo the anaerobic pathway.