Where does beta oxidation occur?

Beta oxidation occurs in the perimitochondrial space in eukaryotic cells. 

Beta oxidation is a multi-step metabolic process in which fatty acid molecules are broken down to generate energy. Fatty acids first cross the cell membrane and enter the cytosol with the help of fatty acid protein transporters. Within the cytosol, the enzyme fatty acyl-CoA synthase adds a CoA group to the fatty acid chain, converting it to acyl-CoA. 

Short acyl-CoA chains enter the mitochondria by diffusing freely through the mitochondrial membrane. Acyl-CoA chains that are too long to enter or be processed in the mitochondria, are broken down by beta oxidation in the peroxisomes. 

Very long acyl-CoA chains are broken down repeatedly until they are eight carbons long. They are then transported into the mitochondria where they enter the beta oxidation cycle. 

In prokaryotic cells, beta oxidation occurs in the cytosol.