The UC San Diego Left-Handed Materials homepage covers a class of manufactured materials that seemingly violate the laws of physics.
A Left-Handed material reverses a basic feature of light: that is, in a Left-handed medium, light propagates (or appears to move) in the opposite direction as energy flows! This leads to some very interesting consequences, such as the reversal of the Doppler shift for radiation, and the reversal of Cherenkov radiation. Russian physicist V. G. Veselago postulated these effects in a paper published in 1964 (translated in 1968). Cherenkov radiation is the light emitted when a charged particle passes through a medium, under certain conditions. In a normal material, the emitted light is in the forward direction, while in the Left-handed medium, light is emitted in the reverse direction.