Influenza A viruses are responsible for seasonal epidemics, and pandemics can arise from the transmission of novel zoonotic influenza A viruses to humans . Influenza A viruses contain a segmented negative-sense RNA genome, which is transcribed and replicated by the viral-RNA-dependent RNA polymerase (FluPol ) composed of PB1, PB2 and PA subunits . Although the high-resolution crystal structure of FluPol of bat influenza A virus has previously been reported , there are no complete structures available for human and avian FluPol . Furthermore, the molecular mechanisms of genomic viral RNA (vRNA) replication-which proceeds through a complementary RNA (cRNA) replicative intermediate, and requires oligomerization of the polymerase -remain largely unknown. Here, using crystallography and cryo-electron microscopy, we determine the structures of FluPol from human influenza A/NT/60/1968 (H3N2) and avian influenza A/duck/Fujian/01/2002 (H5N1) viruses at a resolution of 3.0-4.3 Å, in the presence or absence of a cRNA or vRNA template. In solution, FluPol forms dimers of heterotrimers through the C-terminal domain of the PA subunit, the thumb subdomain of PB1 and the N1 subdomain of PB2. The cryo-electron microscopy structure of monomeric FluPol bound to the cRNA template reveals a binding site for the 3' cRNA at the dimer interface. We use a combination of cell-based and in vitro assays to show that the interface of the FluPol dimer is required for vRNA synthesis during replication of the viral genome. We also show that a nanobody (a single-domain antibody) that interferes with FluPol dimerization inhibits the synthesis of vRNA and, consequently, inhibits virus replication in infected cells. Our study provides high-resolution structures of medically relevant FluPol , as well as insights into the replication mechanisms of the viral RNA genome. In addition, our work identifies sites in FluPol that could be targeted in the development of antiviral drugs.