Pulsar-wind nebulae emit an extremely broad spectrum of continuum radiation, from low radio frequencies to TeV gamma rays. The part of the spectral energy distribution (SED) from radio through MeV gamma rays is due to synchrotron emission from a distribution of relativistic electrons (or pairs) which can be described by one or more power laws. This spectrum exhibits that particle energy distribution, responsible also for the higher-energy (GeV–TeV) part of the SED, due to inverse-Compton upscattering of one of three photon fields: the synchrotron spectrum, the cosmic microwave background, or ambient optical/infrared photons. However, in a few sources, primary hadrons may produce GeV–TeV gamma rays through the decay of neutral pions produced in inelastic cosmic-ray collisions with thermal gas. The higher-energy end of the particle spectrum, producing synchrotron photons above approximately 10 keV, holds clues to the particle acceleration process. However, its detailed study requires imaging spectroscopy in this energy range, not available until the NuSTAR mission beginning in 2012, which performs true imaging between 3 and 78 keV with
angular resolution. I review NuSTAR observations of the first three pulsar-wind nebulae (PWNe) to be examined in this way: the Crab Nebula, G21.5–0.9 and MSH 15–52. All three show spectral structure not previously known: spectral steepening in certain locations and overall source shrinkage with increasing photon energy. The Crab Nebula has different shrinkage rates along the torus and along the northwest counter-jet. The latter rate is similar to that for both the other sources (FWHM
). I discuss implications of these results for models of particle transport in PWNe.