  Context. There is a population of runaway stars that move at extremely high
speeds with respect to their surroundings. The fast motion and the stellar wind
of these stars, plus the wind-medium interaction, can lead to particle
acceleration and non-thermal radiation.
  Aims. We characterise the interaction between the winds of fast runaway stars
and their environment, in particular to establish their potential as cosmic-ray
accelerators and non-thermal emitters.
  Methods. We model the hydrodynamics of the interaction between the stellar
wind and the surrounding material. We self-consistently calculate the injection
and transport of relativistic particles in the bow shock using a multi-zone
code, and compute their broadband emission from radio to $\gamma$-rays.
  Results. Both the forward and reverse shocks are favourable sites for
particle acceleration, although the radiative efficiency of particles is low
and therefore the expected fluxes are in general rather faint.
  Conclusions. We show that high-sensitivity observations in the radio band can
be used to detect the non-thermal radiation associated with bow shocks from
hypervelocity and semi-relativistic stars. Hypervelocity stars are expected to
be modest sources of sub-TeV cosmic rays, accounting perhaps for a $\sim 0.1$%
of that of galactic cosmic rays.
