This paper aims to summarize the developments of high current H2+ and H3+ ion sources in the past decades. The status of the H2+ and H3+ ion sources is discussed to show the attempts researchers made to improve the beam currents of H2+ and H3+. The results of the 2.45 GHz electron cyclotron resonance ion source named PMECR II at Peking University are presented, which may provide an alternative reference for the design and operation of high current H2+ and H3+ ion sources.