Processes that do not require oxygen are referred to as anaerobic processes, a common example of which is fermentation. Fermentation is a process that breaks down sugar molecules without the presence of oxygen. It is an alternative way for cells to manufacture ATP.
Because there was very little oxygen present when the first living cells appeared on Earth, most ancient organisms produced energy through anaerobic respiration. It was only after the first plants produced enough oxygen for it to build up in the atmosphere that the more efficient process of aerobic respiration became prevalent. There are still many anaerobic bacteria on the earth, and anaerobic respiration occurs in many places when oxygen is not available.