The first "Today's Featured Article" (TFA) section on the main page was on February 22, 2004 (Wolfgang Amadeus Mozart, since you ask). Rather than the full article being displayed on the main page, a summary (often described as a "blurb") appears, with a link to the full article appearing in bold. To start with, the rotation of TFAs was done by updating . The selection did not change promptly at midnight UTC as it now does, and sometimes TFAs would appear for more or less than 24 hours.
The system of using daily templates, prepared in advance and automatically transcluded onto the main page, began on August 7, 2004. Since then, things have been a little more regular.
The general rules for the TFA section are these: only featured articles appear; there is only one TFA per day; each one is displayed for 24 hours; and only one image accompanies the blurb. Until a change in early 2017, there was also an additional rule that no FA could appear more than once as TFA. Most of the time the rules have been followed... This is a list of times when something a bit different, intentionally or otherwise, has happened in the TFA section.