Mozilla Firefox is the fourth most popular web browser, (approximately 5.96% desktop market share as of July 2023), which is quite impressive for an open-source project born from the battered corpse of Netscape after it was defeated by Internet Explorer, then stripped and eaten by AOL.
After almost two years since its initial 0.1 release, Mozilla Firefox, or just Firefox, launched version 1.0 on November 9, 2004. Versions 2, 3, and 4 came out in 2006, 2008, and 2011, after which they changed the criteria for being a new version and started to roll out new releases faster. As of June 30, 2022, Firefox 101.0.1 is the official released version for desktops.
Firefox started its life in September 2002 as an experimental branch of the original Mozilla Suite (since discontinued in favor of the community-maintained SeaMonkey) called Phoenix. The Phoenix name ran into trademark issues with Phoenix Technologies, so it was discontinued in favor of Firebird. That name, in turn, was criticized by the developers of the free/open-source Firebird database server, even after Mozilla insisted their browser be called Mozilla Firebird, thus necessitating a second name change. Regardless of what you call it, the browser is mostly known for being hugely and relatively easily customizable through the use of add-ons and scripts, something it inherited from the Mozilla Suite. The email component of the Mozilla suite was refashioned into Firefox's companion, Mozilla Thunderbird.
In November 2017, a revamped version of the browser known as "Firefox Quantum" was released, intended to streamline the browser for the modern era. However, this did not go without controversy, as many well-loved add-ons were deprecated by the new code and had to be rebuilt from scratch.
With most other browsers abandoning their custom rendering engine in favor of Chromium or started as Chromium-powered browser in the first place, Firefox is the rare browser in the market that use its own engine (Safari's WebKit is the basis for Blink in Chromium, so they also share the same root) which in rare cases can expose website incompatibilities either because the dev never bothered to test using non-Chromium browser or there's a DRM component that Firefox refuse to adopt.
For more detailed information, see its page on The Other Wiki. The browser's official webpage can be found here. In addition to the desktop version, Mozilla has also released a mobile version for the Android and iOSnote operating system, which can be downloaded from the Google Play store and Apple App Store, respectively.