Short answers, pulled from the story.
The first unauthorized, non-commercial console emulators began to appear during the mid-1990s. These early programs were often incomplete and only partially emulated a given system, resulting in visible defects.
The first such recognized emulator was released around 1996 as one of the prototype projects that eventually merged into the SNES9X product. Programs like Marat Fayzullin's iNES, VirtualGameBoy, Pasofami, and VSMC became the most popular console emulators of this era.
Sony Computer Entertainment Inc. v. Connectix Corporation in 2000 established that emulators developed through clean room design are legal under United States law. The Librarian of Congress codified these rules as allowed exemptions to bypass technical copyright protections on console hardware under the Digital Millennium Copyright Act.
Phil Spencer stated in November 2021 that he hoped for video game companies to eventually develop legal emulation allowing users to play any past game they already owned a copy of. He characterized this goal as a great North Star for the industry to aim towards in the future.
Microsoft achieved backwards compatibility with popular Xbox titles through emulation starting the 15th of June 2015 when announcing the Xbox One would be compatible with Xbox 360 games. Sony used software emulation to play original PlayStation titles on the PlayStation 3, eventually removing PS2 hardware components to replace them with software emulation.