Most cancer genomic data are generated from bulk samples composed of mixtures of cancer subpopulations, as well as normal cells. Subclonal reconstruction methods based on machine learning aim to separate those subpopulations in a sample and infer their evolutionary history. However, current approaches are entirely data driven and agnostic to evolutionary theory. We demonstrate that systematic errors occur in the analysis if evolution is not accounted for, and this is exacerbated with multi-sampling of the same tumor. We present a novel approach for model-based tumor subclonal reconstruction, called MOBSTER, which combines machine learning with theoretical population genetics. Using public whole-genome sequencing data from 2,606 samples from different cohorts, new data and synthetic validation, we show that this method is more robust and accurate than current techniques in single-sample, multiregion and longitudinal data. This approach minimizes the confounding factors of nonevolutionary methods, thus leading to more accurate recovery of the evolutionary history of human cancers.