Energetic materials are conventionally ignited by the application of heat to some part of an explosive target. This is most often provided by a flame or by electrical heating using a resistive wire. The material responds by thermally heating and starting a burning zone, which spreads out from the ignition point generating gas. In some cases this zone can accelerate (due to the effect of this gas) into a reactive shock wave, termed detonation. Lasers are used in a variety of applications to thermal heat a range of materials, and thus seem an obvious candidate to trigger chemical reaction in energetic ones. A light pulse offers several advantages over an electrical one, since it may be delivered down a path both immune to electrical effects and chemically stable. Thus, the triggering of safety apparatus (such as the firing of bolts on aircraft exits) represents a major thrust in the development of laser-triggered explosive devices. The energy of the pulse may be used in one of two ways to achieve these effects. In the first, the laser is shone directly upon the chemical medium, which absorbs the light at discrete wavelengths. In the second, it is used to vaporize a metallic flyer that is launched to impact on a target creating a high-pressure zone. Either mechanism starts the required reaction. However, when the pulse is delivered directly to the material, detonation is found to proceed immediately with no transition via burning. This makes the process inexplicable using present concepts. This review will address a range of the experiments conducted and theories developed for this novel field. However, it should be emphasized that the fundamental mechanisms remain to be fully explained making the application both academically stimulating as well as industrially important.