Glycolysis does not use molecular oxygen, and occurs in the cytosol of cells.
Glycolysis can happen in aerobic and anaerobic organisms.
It is hypothesized that the reason glycolysis can proceed without molecular oxygen is that the mechanism was initiated before earth s atmosphere contained the element. There has not been any reason for the process to convert to simply aerobic mechanisms. Glycolysis not only produces ATP but also intermediates that are important for biosynthetic processes later on in the metabolic process. The first step involves the phosphorylation of the glucose molecule, by ATP, which creates a sugar phosphate. The glucose molecule stays inside of the cell, due to the negative charges on the phosphate.