Significant use is made of the music of Mozart, Salieri and other composers of the period. The premieres of Mozart's operas The Abduction from the Seraglio, The Marriage of Figaro and The Magic Flute are each the setting for key scenes of the play.

Since the original run, Shaffer has extensively revised his play, including changes to plot details; the following is common to all revisions.

At the opening of the tale, Salieri is an old man, having long outlived his fame, and is convinced he used poison to assassinate Mozart. Speaking directly to the audience, he promises to explain himself. The action then flashes back to the eighteenth century, at a time when Salieri has not met Mozart in person, but has heard of him and his music. He adores Mozart's compositions, and is thrilled at the chance to meet Mozart in person, during a salon at which some of Mozart's compositions will be played. When he finally does catch sight of Mozart, however, he is deeply disappointed to find that Mozart's personality does not match the grace or charm of his compositions. When Salieri first meets him, Mozart is crawling around on his hands and knees, engaging in smutty talk with his future bride Constanze Weber.

Salieri cannot reconcile Mozart's boorish behavior with the genius that God has inexplicably bestowed upon him. Indeed, Salieri, who has been a devout Catholic all his life, cannot believe that God would choose Mozart over him for such a gift. Salieri renounces God and vows to do everything in his power to destroy Mozart as a way of getting back at his Creator.

Throughout much of the rest of the play, Salieri masquerades as Mozart's ally to his face while doing his utmost to destroy his reputation and any success his compositions may have. On more than one occasion it is only the direct intervention of the Emperor himself that allows Mozart to continue (interventions which Salieri opposes, and then is all too happy to take credit for when Mozart assumes it was he who intervened). Salieri also humiliates Mozart's wife when she comes to Salieri for aid, and smears Mozart's character with the Emperor and the court. A major theme in Amadeus is Mozart's repeated attempts to win over the aristocratic "public" with increasingly brilliant compositions, which are always frustrated either by Salieri or by the aristocracy's own inability to appreciate Mozart's genius.

The play ends with Salieri attempting suicide in a last attempt to be remembered, leaving a false confession of having murdered Mozart with arsenic. He survives, however, and his confession is disbelieved by all, leaving him to wallow once again in mediocrity.

Shaffer used artistic license in his portrayals of both Mozart and Salieri. Documentary evidence suggests that there was some antipathy between the two men, but the idea that Salieri was the instigator of Mozart's demise is not given academic credence. While, historically, there may have been actual rivalry between Mozart and Salieri, there is also evidence that they enjoyed a relationship marked by mutual respect. As an example, Salieri later tutored Mozart's son Franz Xaver Wolfgang Mozart in music.

Writer David Cairns called Amadeus "myth-mongering" and argued against Shaffer's alleged portrait of Mozart as "two contradictory beings, sublime artist and fool", positing instead that Mozart was "fundamentally well-integrated". Cairns also rejects the "romantic legend" that Mozart always wrote out perfect manuscripts of works already completely composed in his head, citing major and prolonged revisions to several manuscripts (see: Mozart's compositional method).[citation needed]

Amadeus was first presented at the Royal National Theatre, London in 1979, directed by Sir Peter Hall and starring Paul Scofield as Salieri, Simon Callow as Mozart, and Felicity Kendal as Constanze. It was later transferred in modified form to the West End, starring Frank Finlay as Salieri.

The play premiered on Broadway in 1980 with Ian McKellen as Salieri, Tim Curry as Mozart and Jane Seymour as Constanze. It ran for 1,181 performances and was nominated for seven Tony Awards (best actor for both McKellen and Curry, best director for Peter Hall, best play, best costume design, lighting, and set design for John Bury), of which it won five (including a best actor Tony for McKellen). During the run of the play McKellen was replaced by John Wood, Frank Langella, David Dukes, David Birney, John Horton, and Daniel Davis. Curry was replaced by Peter Firth, Dennis Boutsikaris, John Pankow, Mark Hamill, and John Thomas Waite. Also playing Constanze were Amy Irving, Suzanne Lederer, and Maureen Moore.