Sequencing of nucleic acids with nanopores has emerged as a powerful tool offering rapid readout, high accuracy, low cost and portability. This label-free method for sequencing at the single-molecule level is an achievement on its own. However, nanopores also show promise for the technologically even more challenging sequencing of polypeptides, something that could considerably benefit biological discovery, clinical diagnostics and homeland security, as current techniques lack portability and speed. Here we survey the biochemical innovations underpinning commercial and academic nanopore DNA/RNA sequencing techniques, and explore how these advances can fuel developments in future protein sequencing with nanopores.