Transcriptionally active genes in eukaryotes still retain most of the Chromatin packaging that is characteristic of eukaryotic DNA. Nucleosomes and even some higher order structure are present, although the histones may be chemically modified, for example by acetylation or phosphorylation, as part of the activation process. The presence of nucleosomes on the coding region of active genes raises the question: How does an RNA polymerase transcribe such a template? We have attempted to answer this question with relatively simple model systems involving a template carrying a single positioned nucleosome. We have shown that when a phage polymerase, SP6, transcribes such a template, the histone octamer of the nucleosome is not released into solution. Instead it is retained on the same DNA molecule, but displaced from its original binding site. Further studies have allowed us to propose a detailed model, which appears to hold not only for SP6 but also for transcription by the much larger RNA polymerase III from yeast. Our most recent results, obtained by electron cryomicroscopy, confirm and refine this model.