The concept of readability has had a variable history, moving from a position where it was considered as a very important topic for those responsible for producing texts and matching those texts to the abilities and needs of learners, to its current declining visibility in the education literature. Some important work has been coming from the USA over the past few years, however, which makes it clear that a closer look at the text dimension of the reader-text interface is somewhat overdue. The issue has been redefined as one of text complexity, and there are some significant implications within it for the teaching and development of reading at all phases of learning. In this paper, we try to review some of these implications and suggest their relevance to the UK situation.