About the formulation, verification and validation of the hypersonic flow solver Eilmer. We describe the formulation of the gas dynamics and high-temperature thermochemical modules of the Eilmer code, an open-source Navier-Stokes solver for transient compressible flow in two and three dimensions. The core gas dynamics formulation is based on finite-volume cells, and the thermochemical effects are handled with specialised updating schemes that are coupled into the overall time-stepping scheme. Verification of the code is explored via a number of case studies that use analytic and semi-analytic solutions as comparison. These include both smooth and shocked flows and are used to demonstrate the order of spatial accuracy of the code. Cases include manufactured solutions for rather abstract inviscid and viscous flow, an idealised detonation wave supported by a curved body, and the transient flow of an idealised but high-performance shock tube. Validation of the inviscid gas dynamics and thermochemical models is then explored using data from a selection of experimental studies. These studies include ballistic range experiments with chemically-inert noble gases and high-temperature chemically-reacting air. These comparisons show that the code performs well and they provide a lesson in considering a range of experimental data rather than relying upon isolated data points for validation. These verification and validation cases are described in full detail and will be useful for other code developers of high-temperature compressible flow solvers.