Teaching and learning Shakespeare takes place across the world. Pedagogical matters have been the subject of much discussion in the last few decades. This article begins by reviewing that discussion, showing how different approaches – textual, contextual and active (or performance) – connect with the language of the plays. No study, it is pointed out, has conducted an empirical investigation as to what exactly students find problematic when they read the language of Shakespeare’s plays, an obvious first step, one might think, in designing an approach. The main aim of this article was to describe a study designed to do exactly this. It was conducted with two groups of Shakespeare students, one with English as a first language and one with English as an additional language. Participants were asked to identify difficulties in extracts from plays, rate specific linguistic forms according to difficulty and discuss what they think of Shakespeare’s language. Common areas of difficulty included archaic words, borrowings from other languages, coinages and false friends. With these findings in mind, the article briefly reflects on pedagogical solutions that are corpus-related, arguing that these address some of the problems associated with traditional textual approaches by requiring the active involvement of learners, treating language in a contextualised fashion and focussing on the language itself. © The Author(s) 2020.