The complexity of human language and the apparent limits of the human cognitive system gave rise to the assumption that children must be born with the knowledge of core language principles to make language acquisition feasible. In this seminar, we will discuss how the ideas about Universal Grammar changed in theoretical linguistics, and how computational linguistics challenged the `poverty of the stimulus’ argument. We will explore a number of computational models that `acquire’ different aspects of language with limited input. We will further turn to modern transformer and related artificial neural network architectures and discuss the extent of their linguistic skills. This approach will help us address language learnability as a computational challenge.