The diffeomorphism group of a disc plays a distinguished role in the study of automorphism groups of manifolds, and its homotopy type has been studied by geometric topologists for many years. This talk serves to survey the current knowledge of its rational homotopy groups in high dimensions, and to explain a new computation of these groups in odd dimensions in terms of algebraic K-theory, valid in degrees up to approximately the dimension. The proof builds on recent advances in the study of moduli spaces of high-dimensional manifolds, and is independent of Waldhausen’s work on pseudoisotopy on which Farrell--Hsiang's earlier computation of these groups in the pseudoisotopy stable range relies.