In Greek mythology, the Trojans were the occupants of a city called Troy. The Greeks went to war against Troy because the Trojans kidnapped Helena, the queen of Sparta. The war between the Greeks and the Trojans was called the Trojan war and the largest Trojan asteroids were named after heroes from that war.
Continuing the Trojan-Greek theme of Jupiter's asteroids, those asteroids ahead of Jupiter in its orbit are called the "Greeks" and those behind Jupiter are called the "Trojans". Collectively, they are all referred to as Trojans. So far, astronomers have found and numbered more than 4000 asteroids in these regions, but they believe that more than one million exist, similar to the number of asteroids believed to inhabit the asteroid belt.
Three other planets are known to have Trojan asteroids. Neptune has at least six that have been discovered, but there could be many more. Mars also has four asteroids that occupy Lagrangian points. In October of 2010, scientists discovered 2010 TK7, the first trojan asteroid belonging to earth. Scientists evaluated the orbit May of 2011 and published their findings in July. The 1000 foot diameter object orbits around the L4 Langrangian point, 60 degrees ahead of earth.
Another class of Trojan is called a Trojan moon. A Trojan moon follows or precedes a planet's moon in much the same way a Trojan asteroid follows or precedes a planet. Two of Saturn's moons, Tethys and Dione, each have two Trojan moons and thus far are the only moons in the Solar System known to have Trojan moons. Earth's moon does not have any Trojan moons.