In healthy cells, controlled activation of aurora kinases regulates mitosis. Overexpression and hyperactivation of aurora kinases A and B have major roles in tumorigenesis, and can induce aneuploidy and genomic instability. In squamous-cell carcinomas of the head and neck, overexpression of aurora kinase A is associated with decreased survival, and a reduction in aurora kinase A and aurora kinase B expression inhibits cell growth and increases apoptosis. In this Review, we provide an overview of the biological functions of aurora kinases in healthy cells and in cancer cells, and we review small studies and high-throughput datasets that particularly implicate aurora kinase A in the pathogenesis of squamous-cell carcinomas of the head and neck. Early phase trials are beginning to assess the activity of small-molecule inhibitors of aurora kinases. We summarise trials of aurora kinase inhibitors in squamous-cell carcinomas of the head and neck, and discuss directions for future drug combination trials and biomarkers to use with drugs that inhibit aurora kinases.