When a plane goes faster than the speed of sound, those around it hear a resounding crack that's called a sonic boom. When particles go faster than the speed of light, those around them see a special glow. This is called Cherenkov Radiation. And it's a lot prettier than a sonic boom.
Aircraft traveling through the atmosphere below the speed of sound push air out of the way in a relatively orderly fashion. They may be loud, but they don't boom. Planes traveling above the speed of sound are something else. The air piles up, creating a shock wave, which forms a kind of cone around the aircraft. If you're just ahead of the cone, the air pressure is normal. Once the plane overtakes you, the air just inside the cone is at a much, much higher pressure. That high pressure translates into a boom when it hits your ear.
There is an equivalent to this in light, but it only pops up in certain situations. It's known that nothing can go higher than the speed of light - but the silent addendum to that is "in a vacuum." Only in a vacuum does light reach the universal speed limit. As it travels through different media it is refracted and interacts with the various atoms it comes into contact with. The photon is still going at light speed, but it's trip through the medium is at slightly lower than light speed. The degree to which light speed is reduced is known as the refractive index of the medium. For example, glass has a refractive index of 1.49, so light will go through it at light speed in a vacuum, divided by a factor of 1.49. Diamond has an index of refraction of about 2.42 - so if you're hoping to see light get through a diamond you could probably wait around all day.
Because light is slowed down so much in different media, it's possible for charged particles to move through a medium even faster than light would move through that medium. This happens most often in nuclear reactors, when particles are ejected from a nucleus with such force that they jet through their surroundings faster than light would.
These particles still interact with the medium as they go through, exciting molecules which then release energy by releasing photons. Usually, this wouldn't create enough of a glow to be noticeable, but just like sound waves piling up at the tip of an aircraft, emissions of photons "pile up" as multiple photons are emitted at once. These photons move in phase with one another, and constructively interfere. Their peaks and valleys build on each other to the point where they are visible to the naked eye. This is Cherenkov (or Cerenkov) radiation, and it is emitted in a cone centered on the moving particles. It's a very beautiful glow, but probably not worth looking into a nuclear reactor for.
Top Image: Corey Hines, WSU TRIGA Reactor
Second Image: Matt Howard, Argonne National Laboratory