One contribution of 13 to a theme issue 'New frontiers for statistical learning in the cognitive sciences'. In recent years, statistical learning (SL) research has seen a growing interest in tracking individual performance in SL tasks, mainly as a predictor of linguistic abilities. We review studies from this line of research and outline three presuppositions underlying the experimental approach they employ: (i) that SL is a unified theoretical construct; (ii) that current SL tasks are interchangeable, and equally valid for assessing SL ability; and (iii) that performance in the standard forced-choice test in the task is a good proxy of SL ability. We argue that these three critical presuppositions are subject to a number of theoretical and empirical issues. First, SL shows patterns of modality-and informationalspecificity, suggesting that SL cannot be treated as a unified construct. Second, different SL tasks may tap into separate sub-components of SL that are not necessarily interchangeable. Third, the commonly used forced-choice tests in most SL tasks are subject to inherent limitations and confounds. As a first step, we offer a methodological approach that explicitly spells out a potential set of different SL dimensions, allowing for better transparency in choosing a specific SL task as a predictor of a given linguistic outcome. We then offer possible methodological solutions for better tracking and measuring SL ability. Taken together, these discussions provide a novel theoretical and methodological approach for assessing individual differences in SL, with clear testable predictions.This article is part of the themed issue 'New frontiers for statistical learning in the cognitive sciences'.