Well-resolved large-eddy simulations (LES) are performed in order to investigate flow phenomena and turbulence structure of the boundary layer along a supersonic compression ramp. The numerical simulations directly reproduce an available experimental result. The compression ramp has a deflection angle of $\beta\,{=}\,25^\circ$. The mean free-stream Mach number is $M_\infty\,{=}\,2.95$. The Reynolds number based on the incoming boundary-layer thickness is $Re_{\delta_0}\,{=}\,63\,560$ in accordance with the reference experiment. These simulations overcome deficiencies of earlier direct numerical simulations (DNS) and LES in terms of ramp-deflection angle, Reynolds number and spanwise size of the computational domain which is required for capturing the essential flow phenomena. The filtered conservation equations for mass, momentum and energy are solved with a high-order finite-difference scheme. The effect of subgrid scales is modelled by the approximate deconvolution model. About $18.5\,{\times}\,10^6$ grid points are used for discretizing the computational domain. To obtain mean flow and turbulence structure the flow is sampled 1272 times over 703 characteristic time scales of the incoming boundary layer. Statistical data are computed from these samples. An analysis of the data shows good agreement with the experiment in terms of mean quantities such as shock position, separation and reattachment location, skin-friction and surface-pressure distributions, and turbulence structure. The computational data confirm theoretical and experimental results on fluctuation amplification across the interaction region. In the wake of the main shock a shedding of shocklets is observed. The temporal behaviour of the coupled shock–separation system agrees well with experimental data. Unlike previous DNS the present simulation data provide indications of a large-scale shock motion. Also, evidence for the existence of three-dimensional large-scale streamwise structures, commonly referred to as Görtler-like vortices, is found.