From three aspects of metal foil bridge electrical explosion, electrical explosion drive flyer and flyer shock initiation explosive, the research progress in the function mechanism of exploding foil initiators was reviewed. It is considered that the exploding foil initiators have made important progress in the sectional resistivity model, advanced flyer velocity measurement technology, calculation model of the electrical explosion drive flyer velocity based on the energy conversion coefficient and the sensitivity prediction based on the critical initiation criterion etc aspects. Some regular knowledges have been obtained and the low energy design is promoted to some extent. It is pointed out that the quantitative description of energy dissipation and flyer ablation, temporal shape of the flyer in the flight, non-ideal detonation performance prediction at small scale and the micro reaction flow observation technology after the wave front will become the key points in the future research of exploding foil initiators in the electrical explosion drive flyer process under the small size condition.