Neutron scattering and muon spectroscopy are techniques that use subatomic particles to understand materials across a wide range of energy (μeV to tens of eV), length (Å to cm) and time (attosecond to hour) scales. The methods are widely used to study condensed phase materials in areas that span physics, chemistry, biology, engineering and cultural heritage. In this Perspective we consider three questions: (i) will neutron scattering and muon spectroscopy still be needed in the 2050s? (ii) What might the technology to produce neutron and muon beams look like in the 2050s? (iii) What will be the applications in the 2050s? Overall, the neutron/muon ecosystem in the 2050s will have less capacity than now, but greater capability because of the somewhat higher power sources, better instrumentation and data analysis.