The influenza A viruses are the causative agents of respiratory disease that occurs as yearly epidemics and occasional pandemics. These viruses are endemic in wild avian species and can sometimes break the species barrier to infect and generate new virus lineages in humans. The influenza A virus genome consists of eight single-stranded, negative-polarity RNAs that form ribonucleoprotein complexes by association to the RNA polymerase and the nucleoprotein. In this review we focus on the structure of this RNA-synthesis machines and the included RNA polymerase, and on the mechanisms by which they express their genetic information as mRNAs and generate progeny ribonucleoproteins that will become incorporated into new infectious virions. New structural, biochemical and genetic data are rapidly accumulating in this very active area of research. We discuss these results and attempt to integrate the information into structural and functional models that may help the design of new experiments and further our knowledge on virus RNA replication and gene expression. This interplay between structural and functional data will eventually provide new targets for controlled attenuation or antiviral therapy.