Metal organic frameworks (MOFs) are porous crystalline solids whose frameworks are constituted by metal ions/nodes with rigid organic linkers leading to the formation of materials having high surface area and pore volume. One of the unique features of MOFs is the presence of coordinatively unsaturated metal sites in their crystalline lattice that can act as Lewis acid sites promoting organic transformations, including aerobic oxidation reactions of various substrates such as hydrocarbons, alcohols, and sulfides. This review article summarizes the existing Co-based MOFs for oxidation reactions organized according to the nature of substrates like hydrocarbon, alcohol, olefin, and water. Both aerobic conditions and peroxide oxidants are discussed. Emphasis is placed on comparing the advantages of using MOFs as solid catalysts with respect to homogeneous salts in terms of product selectivity and long-term stability. The final section provides our view on future developments in this field.