Ace Combat Infinity is set in an alternate timeline, in which Earth was ravaged by the "Ulysses Disaster". In 1994, a fictional asteroid collides with one of Jupiter's moons, 5254 Ulysses. This event sends about 10,000 meteors heading for Earth, all expected to impact the planet in five years' time. Faced with the prospect of extinction, the world's major superpowers build "Stonehenge", a network of anti-air railguns across the planet. The meteor storm finally hits Earth in July 1999. While Stonehenge destroys enough of the inbound meteors to prevent human extinction, the remaining meteors still ravaged about 20% of the Earth's surface, destabilizing the economy and collapsing the world order. The disaster hits Europe and Asia especially hard, forcing the nations to reorganize and create automated refugee zones. Twenty years later, the United Nations Forces finds itself fighting against terrorist organizations around the world. To better combat the terrorist threat, the UN hires Arrows Air Defense and Security, a private military company specializing in aerial warfare.
The player character and silent protagonist, callsign "Reaper", is a rookie pilot employed by Arrows. Arrows assigns Reaper to the "Bone Arrow" squadron, which includes long-time pilot "Omega" and ace veteran "Viper". Part-way through the story, Bone Arrow becomes rivals with Ridgeback Squadron, a squadron of elite UNF pilots headed by leader "Slash" and his second-in-command, "Edge". The main antagonist forces are the Sons of Troia, a group of armed terrorists who later create an independent "Federation of USEA" or USEA Federation. Reaper's actions against the Sons of Troia and USEA soon make him a recognized mercenary ace pilot.
Elements in the game, such as the Ulysses disaster, the Stonehenge superweapon and the rise of the USEA enemy faction (a new multinational military federation (the "United States of EurAsia"), rather than a fictional continent), are direct references to Ace Combat 4: Shattered Skies, but played on Earth instead of "Strangereal", the fictional planet setting of previous Ace Combat games. Furthermore, the player character taking the role of a mercenary pilot of a private military company hired by the UN to keep the "post-Ulysses" world stable to regional dispute and terrorism attacks, is similar to the storyline of Ace Combat Zero: The Belkan War. Other elements, including fictional aircraft, names of locales and specific mission settings, reference elements of previous games in the franchise.