The ability to manipulate structure and properties using pressure has been well known for many centuries. Diffraction provides the unique ability to observe these structural changes in fine detail on lengthscales spanning atomic to nanometre dimensions. Amongst the broad suite of diffraction tools available today, neutrons provide unique capabilities of fundamental importance. However, to date, the growth of neutron diffraction under extremes of pressure has been limited by the weakness of available sources. In recent years, substantial government investments have led to the construction of a new generation of neutron sources while existing facilities have been revitalized by upgrades. The timely convergence of these bright facilities with new pressure-cell technologies suggests that the field of high-pressure (HP) neutron science is on the cusp of substantial growth. Here, the history of HP neutron research is examined with the hope of gleaning an accurate prediction of where some of these revolutionary capabilities will lead in the near future. In particular, a dramatic expansion of current pressure-temperature range is likely, with corresponding increased scope for extreme-conditions science with neutron diffraction. This increase in coverage will be matched with improvements in data quality. Furthermore, we can also expect broad new capabilities beyond diffraction, including in neutron imaging, small angle scattering and inelastic spectroscopy.