The mammalian nucleus is filled with self-organizing, nanometer-scale nucleoprotein machines that carry out DNA replication, RNA biogenesis and DNA repair. We discuss, as a model, the nonhomologous end-joining (NHEJ) machine, which repairs DNA double-strand breaks. The NHEJ machine consists of six core polypeptides and 10-20 ancillary polypeptides. A full understanding of its design principles will require measuring the behavior of single NHEJ complexes in living cells, using a Nano Toolbox that includes bright, stable, biocompatible fluorophores, efficient protein and nucleic acid-tagging strategies, and sensitive, high-resolution imaging methods. Taking inspiration from natural examples, it might be possible to adapt and redesign the NHEJ machine to precisely correct mutations responsible for common human diseases, such as K-ras in lung cancer or human papillomavirus E6 and E7 genes in cervical and oral cancers.