Angels in America focuses on the stories of two troubled couples, one gay, one straight: "word processor" Louis Ironson and his lover Prior Walter, and Mormon lawyer Joe Pitt and his wife Harper. After the funeral of Louis's grandmother, Prior tells him that he has contracted AIDS, and Louis panics. He tries to care for Prior but soon realizes he cannot stand the strain and fear. Meanwhile, Joe is offered a job in the Justice Department by Roy Cohn, his right-wing, bigoted mentor and friend. But Harper, who is addicted to Valium and suffers anxiety and hallucinations, does not want to move to Washington.

The two couples' fates quickly become intertwined: Joe stumbles upon Louis crying in the bathroom of the courthouse where he works, and they strike up an unlikely friendship based in part on Louis's suspicion that Joe is gay. Harper and Prior also meet, in a fantastical mutual dream sequence in which Prior, operating on the "threshold of revelation," reveals to Harper that her husband is a closeted homosexual. Harper confronts Joe, who denies it but says he has struggled inwardly with the issue. Roy receives a different kind of surprise: At an appointment with his doctor Henry, he learns that he too has been diagnosed with AIDS. But Roy, who considers gay men weak and ineffectual, thunders that he has nothing in common with them—AIDS is a disease of homosexuals, whereas he has "liver cancer." Henry, disgusted, urges him to use his clout to obtain an experimental AIDS drug.

Prior's illness and Harper's terrors both grow worse. Louis strays from Prior's bedside to seek anonymous sex in Central Park at night. Fortunately, Prior has a more reliable caretaker in Belize, an ex-drag queen and dear friend. Prior confesses to Belize that he has been hearing a wonderful and mysterious voice; Belize is skeptical, but once he leaves we hear the voice speak to Prior, telling him she is a messenger who will soon arrive for him. As the days pass, Louis and Joe grow closer and the sexual tinge in their banter grows more and more obvious. Finally, Joe drunkenly telephones his mother Hannah in Salt Lake City to tell her that he is a homosexual, but Hannah tells him he is being ridiculous. Nonetheless, she makes plans to sell her house and come to New York to put things right. In a tense and climactic scene, Joe tells Harper about his feelings, and she screams at him to leave, while simultaneously Louis tells Prior he is moving out.

The disconsolate Prior is awakened one night by the ghosts of two ancestors who tell him they have come to prepare the way for the unseen messenger. Tormented by such supernatural appearances and by his anguish over Louis, Prior becomes increasingly desperate. Joe, equally distraught in his own way, tells Roy he cannot accept his offer; Roy explodes at him and calls him a "sissy." He then tells Joe about his greatest achievement, illegally intervening in the espionage trial of Ethel Rosenberg in the 1950s and guaranteeing her execution. Joe is shocked by Roy's lack of ethics. When Joe leaves, the ghost of Ethel herself appears, having come to witness Roy's last days on earth. In the climax of Part One, Joe follows Louis to the park, then accompanies him home for sex, while Prior's prophetic visions culminate in the appearance of an imposing and beautiful Angel who crashes through the roof of his apartment and proclaims, "The Great Work begins."

In Part Two, Harper indulges in the fantasy that she is in Antarctica with her imaginary companion Mr. Lies. But Antarctica turns out to be Brooklyn's Prospect Park, and she is picked up by the police. With Joe nowhere to be found, Hannah comes to her rescue, tending to her in the depths of depression. She finally insists that Harper join her at the Mormon Visitor's Center, where she has begun to volunteer. Meanwhile, the increasingly sick Roy checks in to the hospital where Belize works as a nurse. Roy insults him with cutting, racist remarks, but Belize, angry but filled with involuntary respect, gives him valuable advice on his treatment. Their relationship is always bitter but heated and icy by turns. Belize, however, demonstrates his considerable compassion for Prior, who tells him the full story of the Angel's visit. After her dramatic arrival, she gives Prior a prophetic book and explains that she seeks his help to halt the migratory tendency of human beings, which the Angels in Heaven believe tempted God to abandon them. God, she explains, left Heaven forever on the day of the San Francisco earthquake in 1906, and since then his Angels—whose vast powers are fueled by constant sexual activity—have been rudderless and alone. To reverse the trend, the Angel says humans must end their constant motion, their addiction to change. Not surprisingly, Prior is aghast at her words and vows to flee from her at all costs.

Roy learns that his political opponents plan to disbar him for an ethical lapse, but he vows to remain a lawyer until he dies. In a friendly rapprochement, he gives Joe his blessing, until Joe reveals that he has left Harper for a man—he has been living for a blissful month with Louis. Stunned and angry, he demands that Joe end his gay relationship at once. Ethel comes to observe him in his misery. Joe's wife, on the other hand, spends her days at the Mormon Visitor's Center watching a diorama of the Mormon migration featuring a father dummy who looks suspiciously like Joe. When Prior drops in to conduct research on angels, a fantasy sequence ensues in which Louis and Joe appear in the diorama. The formerly silent Mormon mother comes to life and leaves with Harper, giving her painful but valuable advice on loss and change.

Louis and Joe's idyll draws to an end when Louis says he wants to see Prior again. At their meeting, Prior coldly insists that he must present visible proof of his internal bruises. Belize later tells Louis about Joe's relationship with Roy, whose politics and personal history Louis despises. When Louis angrily confronts Joe, their fight turns physical and Joe punches him. He apologizes, horrified, but they never speak again. Roy nears his end as well, reeling from Joe's disclosure and from Ethel's news that he has been disbarred. He dies, but not before tricking Ethel into tenderly singing for him. After his death, Belize summons Louis to recite the Kaddish, the Jewish prayer for the dead, to demonstrate thanks (for his stash of AIDS drugs) and forgiveness. Ethel leads Louis in the prayer, the play's emotional and moral climax.

After Prior suffers an episode at the visitor's center, Hannah takes him to the hospital. There, the Angel descends, and Prior wrestles her. He succeeds, and is granted entry into Heaven to refuse his prophecy. In Heaven, which resembles San Francisco after the great earthquake, Prior tells the Angels that despite all his suffering he wants them to bless him and give him more life. The Angels sympathize but say they cannot halt the plague. He tells them should God return, they should sue Him for abandonment. Back on earth, his fever broken, Prior tells Louis he loves him but that he cannot ever come back. Harper leaves Joe for the last time and sets off on an optimistic voyage to San Francisco to begin her own life.

In 1990, four years later, Louis, Prior, Belize and Hannah appear in a moving epilogue. Prior says that the disease has killed many but that he intends to live on, and that the "Great Work" will continue.