This is a brief survey of the studies of PIE vowel system. The traditionally desciibed and generally accepted system for PIE was Brugmann-Hirt-Meillet``s. De Saussure``s system is different from the others in positing two abstract phonemes, A,Q, in the system. These were deduced from the exhaustive investigations of the ahlaut phenomena, and were described as coefficients sonantiques like the syllabics r I I-Its insightful proposals, however, were not generally accepted until the Hittite documents were discovered and deciphered. The Hittite phonemes showed the regular correspondances to the A,Q. Then most of the IE comparativists devoted themselves to study the laryngeals. The laryngeal theory has been developed, the approaches to which have been three ways. First, some add certain results from the Hittite resources to the laryngeals as coefficients sonantiques. Second, others construct the theory only with reference to the Hittite. Third, others make phonological approaches to the laryngeals with parellel to the Hittite. The writer sketched out these approaches. Finally, according to Keiler(1970), some Hittite phonemes were interpreted as the reflexes of the TE laryngeals, appearing to be a natural consequenses of the kinds of distinctive features.