Short answers, pulled from the story.
Jupiter trojans are a large group of asteroids that share Jupiter's orbit around the Sun, clustered at the L4 and L5 Lagrange points sixty degrees ahead of and sixty degrees behind the planet. Their average semi-major axis is about 5.2 AU from the Sun. More than 15,300 have been confirmed, with the true population estimated in the millions for objects larger than 1 km.
The first accepted Jupiter trojan, 588 Achilles, was discovered in February 1906 by Max Wolf at the Heidelberg-Königstuhl State Observatory. E. E. Barnard had recorded an observation of what turned out to be a trojan (12126 Chersidamas) in 1904, but its identity was not recognized until 1999.
The naming convention was proposed by Johann Palisa of Vienna, who was the first to calculate accurate orbits for these asteroids. Asteroids in the leading L4 swarm are named after Greek heroes, while those in the trailing L5 swarm are named after Trojan heroes. In 2018 the International Astronomical Union expanded the convention to include Olympic and Paralympic athletes for smaller trojans, because known Trojan War figures were running out.
The largest Jupiter trojan is 624 Hektor, with a mean diameter of 203 plus or minus 3.6 km. Hektor is probably a contact binary with a small moonlet. It belongs to the leading L4 swarm and was discovered in 1906-1907 by August Kopff.
Two main theories exist. One holds that planetesimals near Jupiter were captured during its rapid growth phase about 10,000 years long, when Jupiter's mass increased tenfold. The more widely discussed theory links trojan capture to the Nice model, in which planetary instability 500-600 million years after the solar system's formation caused Uranus and Neptune to scatter objects inward, with some being captured at Jupiter's Lagrange points as the giant planets' orbits stabilized.
NASA's Lucy spacecraft, launched on the 16th of October 2021, is set to visit seven Jupiter trojans. It will arrive at the first trojans in 2027 after two Earth gravity assists and a flyby of a main-belt asteroid. Its final destination in the L5 swarm is the binary trojan 617 Patroclus.