Work with the discrete sequence production (DSP) task has provided a substantial literature on discrete sequencing skill over the last decades. The purpose of the current article is to provide a comprehensive overview of this literature and of the theoretical progress that it has prompted. We start with a description of the DSP task and the phenomena that are typically observed with it. Then we propose a cognitive model, the dual processor model (DPM), which explains performance of (skilled) discrete key-press sequences. Key features of this model are the distinction between a cognitive processor and a motor system (i.e., motor buffer and motor processor), the interplay between these two processing systems, and the possibility to execute familiar sequences in two different execution modes. We further discuss how this model relates to several related sequence skill research paradigms and models, and we outline outstanding questions for future research throughout the paper. We conclude by sketching a tentative neural implementation of the DPM.