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The biases of individual language learners act to determine the learnability and cultural stability of languages: learners come to the language learning task with biases which make certain linguistic systems easier to acquire than others. These biases are repeatedly applied during the process of language transmission, and consequently should effect the types of languages we see in human populations. Understanding the cultural evolutionary consequences of particular learning biases is therefore central to understanding the link between language learning in individuals and language universals, common structural properties shared by all the world’s languages. This paper reviews a range of models and experimental studies which show that weak biases in individual learners can have strong effects on the structure of sociallylearned systems such as language, suggesting that strong universal tendencies in language structure do not require us to postulate strong underlying biases or constraints on language learning. Furthermore, understanding the relationship between learner biases and language design has implications for theories of the evolution of those learning biases: models of gene-culture coevolution suggest that, in situations where a cultural dynamic mediates between properties of individual learners and properties of language in this way, biological evolution is unlikely to lead to the emergence of strong constraints on learning.