Abstract: Why only human-beings acquired complex cultural traits? In this research, we survey the theories on cumulative cultural evolution that has been dealing with this question. This is important because cultural evolution is so interdisciplinary a research field as not able to sufficiently systematize existing methods even though we focused only on cumulative and theoretical aspects. In order for terse classification, preceding researches were arranged according to two criteria chronological and methodological. As a result, the former depicted, as already pointed out by Horiuchi (2012), that the current theoretical approach is largely based on learning hypothesis and population hypothesis. On the other hand, the latter suggested the circumstances where methods are still miscellaneous and arbitrarily set to obtain predetermined conclusions. Therefore, this survey concludes it is necessary for agents’ learning and inheritance process to have the consistent assumptions supported by empirical studies. While there are potential constraints, working on this issue with reference to other disciplines would strongly contribute to the further development of theoretical research on cumulative cultural evolution.