Influenza viruses cause seasonal epidemics and pandemic outbreaks associated with significant morbidity and mortality, and a huge cost. Since resistance to the existing anti‐influenza drugs is rising, innovative inhibitors with a different mode of action are urgently needed. The influenza polymerase complex is widely recognized as a key drug target, given its critical role in virus replication and high degree of conservation among influenza A (of human or zoonotic origin) and B viruses. We here review the major progress that has been made in recent years in unravelling the structure and functions of this protein complex, enabling structure‐aided drug design toward the core regions of the PA endonuclease, PB1 polymerase, or cap‐binding PB2 subunit. Alternatively, inhibitors may target a protein–protein interaction site, a cellular factor involved in viral RNA synthesis, the viral RNA itself, or the nucleoprotein component of the viral ribonucleoprotein. The latest advances made for these diverse pharmacological targets have yielded agents in advanced (i.e., favipiravir and VX‐787) or early clinical testing, besides several experimental inhibitors in various stages of development, which are all covered here.