This paper discusses research that has been carried out on maturational constraints for SLA, specifically on the conceptualisation formulated in the critical period hypothesis (CPH). Our review shows that the positions taken by researchers are very diverse, something we believe has its basis in a lack of explicit hypothesis formulation and the use of insufficiently sensitive research instruments. Researchers disagree whether all, only some, or no learners can reach native-like ultimate attainment in a second language. We conclude that there is strong support for maturational constraints, although the CPH itself cannot be maintained in its original formulation. We also propose a unitary interpretation of existing empirical results based on the observation that learners who have been identified as indistinguishable from native speakers characteristically exhibit non-native features that are unperceivable except in detailed and systematic linguistic analyses.