Selective benzyl alcohol oxidation (BA) to benzaldehyde has been frequently used as a benchmark reaction to evaluate the catalytic activity of metal organic frameworks (MOFs) as oxidation catalysts. Substituted BAs, and aliphatic and allylic alcohols have also been often used as substrates in these studies. In the present review, the current state of the art of MOFs as heterogeneous catalysts for the oxidation of BA and other alcohols is described, grouping the reports according to the nature of the active sites present on the MOFs. Thus, MOFs in which the catalytic centres are located at the ligands, at metallic nodes, or at metal nanoparticles (MNPs) incorporated within the MOF pores and photoassisted oxidations have been commented on. The aim of this review is to stress the current limitations encountered in the use of MOFs, particularly with respect to MOF stability and activity and propose new targets in the area.