This review paper concerns allylic oxidations and oxidative dehydrogenations. The corresponding catalysts often contain two or several oxide phases. The objective is to discuss the possible reasons why these phases cooperate (act synergetically). Different interpretations are reviewed. The authors discuss in detail the evidence showing that the synergy is often due to remote control. In such a mechanism, one phase, the donor, dissociates oxygen to form a surface mobile species which spills over to the other phase, or acceptor. The acceptor is the potentially active phase. This phase needs to be irrigated by spill-over oxygen to exhibit maximum activity and selectivity. The various modifications of the acceptor brought about by spill-over oxygen are discussed: maintaining the acceptor at a high oxidation state, preventing the destruction of the structure of the acceptor, and inhibiting the formation of carbonaceous deposits or coke precursors. Parallel experiments with the same two-phase catalysts catalysing an oxygen aided dehydration suggest that the role of spill-over oxygen is to protect some Bronsted acidity of the acceptor. This interpretation of the cooperation between phases permits definite roles to be attributed to the oxide phases present in multicomponent catalysts and to measure approximately their ability to act as donors or acceptors.