The increasing availability of large digital corpora of cross-linguistic data is revolutionizing many branches of linguistics. Overall, it has triggered a shift of attention from detailed questions about individual features to more global patterns amenable to rigorous, but statistical, analyses. This engenders an approach based on successive approximations where models with simplified assumptions result in frameworks that can then be systematically refined, always keeping explicit the methodological commitments and the assumed prior knowledge. Therefore, they can resolve disputes between competing frameworks quantitatively by separating the support provided by the data from the underlying assumptions. These methods, though, often appear as a 'black box' to traditional practitioners. In fact, the switch to a statistical view complicates comparison of the results from these newer methods with traditional understanding, sometimes leading to misinterpretation and overly broad claims. We describe here this evolving methodological shift, attributed to the advent of big, but often incomplete and poorly curated data, emphasizing the underlying similarity of the newer quantitative to the traditional comparative methods and discussing when and to what extent the former have advantages over the latter. In this review, we cover briefly both randomization tests for detecting patterns in a largely model-independent fashion and phylolinguistic methods for a more model-based analysis of these patterns. We foresee a fruitful division of labor between the ability to computationally process large volumes of data and the trained linguistic insight identifying worthy prior commitments and interesting hypotheses in need of comparison. © The Author(s) 2018. Published by Oxford University Press. All rights reserved.