The vast majority of the pulsars detected by the Fermi Large Area Telescope (LAT) display spectra with exponential cutoffs falling in a narrow range around a few GeV. Early spectral modelling predicted spectral cutoff energies of up to 100 GeV. More modern studies estimated spectral cutoff energies in the 1-20 GeV range. It was therefore not expected that pulsars would be visible in the very-high-energy (VHE; >100 GeV) regime. The VERITAS detection (confirmed by MAGIC) of pulsed emission from the Crab pulsar up to 400 GeV (and now possibly up to 1 TeV) therefore raised important questions about our understanding of the electrodynamics and local environment of pulsars. H.E.S.S. has now detected pulsed emission from the Vela pulsar in the 20-120 GeV range, making this the second pulsar detected by a ground-based Cherenkov telescope. We will review the latest developments in VHE pulsar science, including an overview of recent observations and refinements to radiation models and magnetic field structures. This will assist us in interpreting the VHE emission detected from the Crab and Vela pulsars, and predicting the level of VHE emission expected from other pulsars, which will be very important for the upcoming CTA.
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