Alison M. W. Mitchell, Samuel T. Spencer

Pulsar wind nebulae (PWNe), formed when the wind originating from a rapidly rotating neutron star flows out into its surroundings, have now been observed across the electromagnetic spectrum from the radio to the PeV gamma-ray regime. For most of these sources, leptonic processes, where electrons interacting with background photon fields produce high-energy photons through inverse Compton scattering, are believed to be the origin of associated very-high-energy gamma-ray emission. As such, these objects cannot contribute significantly to the galactic hadronic cosmic ray flux at ~TeV-PeV energies. However, in a handful of cases, the possibility for an energetically sub-dominant hadron population being accelerated and producing very to ultra-high energy gamma-rays through pion decay has not yet been comprehensively excluded. Such scenarios have received renewed attention in the light of recent results from the Large High Altitude Air Shower Observatory (LHAASO). In this review we explore the theoretical background positing hadronic acceleration in galactic PWNe, considering cases where the hadrons escape from the pulsar surface and/or are accelerated in the wind, as well as potential 'shock mixing' scenarios. We also explore current and future possible constraints on a hadronic component to PWNe from observations.