Influenza virus mRNAs are stable and competent for nuclear export and translation because they receive a 5´ cap(1) structure in a process called cap snatching1. During cap snatching, the viral RNA-dependent RNA polymerase (FluPol) binds to host RNA polymerase II (Pol II) and the emerging transcript2,3. The FluPol endonuclease then cleaves a capped RNA fragment that subsequently acts as a primer for the transcription of viral genes4,5. Here we present the cryogenic electron microscopy structure of FluPol bound to a transcribing Pol II in complex with the elongation factor DSIF in the pre-cleavage state. The structure shows that FluPol directly interacts with both Pol II and DSIF, positioning the FluPol endonuclease domain near the RNA exit channel of Pol II. These interactions are important for the endonuclease activity of FluPol and FluPol activity in cells. A second structure, trapped after cap snatching, shows that the cleaved capped RNA rearranges within FluPol, directing the capped RNA 3´ end toward the FluPol polymerase active site for viral transcription initiation. Together, our results provide the molecular mechanisms of co-transcriptional cap snatching by FluPol.