Abstract: The article compares the author's work on modeling historical processes, completed 30 years ago, with the publication of a similar model devoted to some hypotheses of the penetration of the “steppe heritage” into the gene pool of European farmers of the Bronze Age. The changes that have occurred in the computer modeling of historical processes, which significantly increase their research potential, are characterized. On the example of the models under consideration, it is discussed in what aspects they help to clarify and develop knowledge about the past. The features of spatially explicit models, which are a subset of imitation models (simulations), are demonstrated, including the possibility of taking into account the genetic parameters of the modeled populations and subsequent comparison with aDNA. The degree of novelty of the results obtained in the two compared models is estimated. It is noted which results of the latest research and additional considerations should be taken into account in order to further bring the behavior of the model closer to reality. It is suggested that the modeling results make it possible to associate the origin of the “steppe heritage” not so much with the population of the Yamnaya culture, but with the contact zone in the south of Ukraine, where interaction with the late Trypillian and other agricultural cultures took place. The necessity of supporting with models any assumptions about historical processes that does not follow directly from empirical material in order to confirm the fundamental reproducibility of the proposed scenario is substantiated.