Cosmic explosions dissipate energy into their surroundings on a very wide range of time-scales: producing shock waves and associated particle acceleration. The historical culprits for the acceleration of the bulk of Galactic cosmic rays are supernova remnants: explosions on ~10000 year time-scales. Increasingly however, time-variable emission points to rapid and efficient particle acceleration in a range of different astrophysical systems. Gamma-ray bursts have the shortest time-scales, with inferred bulk Lorentz factors of ~1000 and photons emitted beyond 100 GeV, but active galaxies, pulsar wind nebulae and colliding stellar winds are all now associated with time-variable emission at ~TeV energies. Cosmic photons and neutrinos at these energies offer a powerful probe of the underlying physical mechanisms of cosmic explosions, and a tool for exploring fundamental physics with these systems. Here we discuss the motivations for high-energy observations of transients, the current experimental situation, and the prospects for the next decade, with particular reference to the major next-generation high-energy observatory CTA.
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