The process that occurs in yeast cells when there is not enough oxygen is called fermentation. This occurs through the process of Anaerobic respiration where instead of using oxygen, organic and inorganic molecules are used as final electron acceptors. Anaerobic refers to the absence of oxygen.
Fermentation is commonly used in lactic acid (in muscles) and alcohol (beers, whiskey) fermentation where the by-product is ethanol. When yeasts are in the process of fermentation, they convert sugars into alcohols or acetic acids.