We all know that accelerated charged particles emit light - that's how modern high-intensity light sources, synchrotrons, function. Interestingly, uniformly moving particles can emit light too.
The idea goes back to the 1904 Sommerfeld's paper, where he studied the motion of charged particles in a vacuum, and demonstrated that particles flying faster than the speed of light emit radiation even when moving uniformly . Of course, the special relativity theory that appeared next year, rendered Sommerfeld's discovery just a funny mathematical result that has nothing to do with reality, since according to the special relativity no particle can move faster than light in a vacuum.
It's worth noting that the velocity restrictions imposed by the special relativity apply only to a single particle (a group velocity of a bunch of particles can be anything) moving in a vacuum (the speed of light in a medium is much smaller than in a vacuum and particles can move faster than that). However, it took more than 30 years to generalize the Sommerfeld idea to the case of charged particles propagating through a material.
Pavel Cherenkov was pursuing a PhD under Sergey Vavilov, a brother of a famous geneticist Nikolai Vavilov (who was imprisoned and eventually killed by the Soviet regime). Cherenkov was studying the luminescence of uranium salts in solutions irradiated by gamma-rays, and was quite surprised to see the "luminescence" of a pure liquid (sulfuric acid it was), with no salts added. Actually, he was convinced that his PhD work was completely ruined .
And it was Vavilov who suggested that this radiation was not luminescence but something completely new, and encouraged Cherenkov to continue the measurements. Indeed, very soon Igor Tamm and Ilya Frank developed a theory for the effect, showing that the radiation is emitted by electrons propagating faster than the speed of light in this particular solution. In 1958 Cherenkov, Tamm, and Frank shared a Nobel Prize for this discovery (unfortunately, without Vavilov who deceased in 1951).
Although Russians call it the "Vavilov-Cherenkov effect", it seems that the name of Vavilov is omitted in the rest of the world where people simply refer to the "Cherenkov Radiation". Why do they?
The funny thing is that immediately after the discovery Vavilov (himself) wrote a paper and submitted it to Nature, where it was rejected (!), and then to Physical Review. This paper had a single author - Cherenkov .
I wonder whether such an extreme academic generosity would be possible nowadays :-)
 A. Sommerfeld, Göttingen Nachrichten 9, 363 (1904); 201 (1905)
 V. L. Ginsburg "About science and about myself" (2001)
 P. A. Čerenkov, Phys. Rev. 52, 378 (1937)