Antony is living in Egypt, and is happy to be infatuated with Cleopatra. Everything in Egypt is going great, and then Antony gets word that things are falling apart in Rome. He hears that wars are brewing, and it’s clear that the other two triumvirs, Lepidus and Caesar, could really use his help. Most importantly, Antony hears rumors that he’s losing face in Rome for being the Queen of Egypt’s pet. He resolves to go home and be a soldier once more.
In Rome, straits are dire. Wars are being waged left and right, and as soon as Antony resolves one issue, another pops up. Antony's wife and brother are battling Caesar, which gets resolved when Antony's wife dies. In a war between Pompey and the Roman triumvirs, Antony negotiates a truce with Pompey, which also resolves the pirate issue. Everything comes to a head, though, when Antony marries Octavia, thinking this seals his peace with Caesar, only to find out that Caesar has betrayed him by breaking the truce with Pompey, kicking Lepidus out of office, and speaking ill of Antony publicly. Antony can’t abide by these wrongs, and so decides to go to war against Caesar. The first battle will be held at sea. Antony is supposed to have Cleopatra’s aid, but when the naval battle comes to a head, Cleopatra’s ship flees. Antony, out of his love for her, follows. He feels he’s undone as a soldier, never mind having lost the battle.
Things are going badly for Antony. Cleopatra flirts with Caesar’s messenger, Thidias, which shows her compromised love and loyalty to Antony. This is a particularly awful blow, as he’s just lost a naval battle and his soldierly honor for her love, thinking it was true. Some of the men on watch hear strange music all around them, which they interpret to be the sound of Hercules abandoning Antony. Most strikingly, Enobarbus deserts Antony for Caesar’s camp. The sum of these little blows is Antony’s admission that he’s losing faith in himself, which doesn’t bode well for how he’ll come out in battle. If he doesn’t even believe he’ll triumph, then how can anyone else?
We might think Antony’s finally come to his senses. He watches his own men turn against him at sea, and is convinced this is the work of Cleopatra’s betrayal. When he hunts her down, we see that his real conflict isn’t all the wars (which he’s used to as a soldier), but the question of whether Cleopatra is as devoted to him as he is to her, given that he’s sacrificed so much for this woman. It seems that, in spite of all the hot and cold feelings, this time he’s really had it, and we’re not sure what he’ll do.
Cleopatra goes through with this little ruse to gain Antony’s attention. Like she usually does, she plans to decide her actions based on his reactions (slightly backwards, isn’t it?). She doesn’t anticipate how far he’s fallen into despair, but the audience knows they can expect something awful, given how things have been going.
Antony relents his fury, and lets love take him to suicide, thinking he’ll find Cleopatra in death. His suicide isn’t a sad one inherently: he does it because he feels it’s the best way to prove that he, and not Caesar, is the sole master of his own destiny. In that regard, it’s a noble and very self-possessed act. With this in mind, his death scene isn’t a lamentable one, though it is tragic. Cleopatra says she’ll kill herself, too, though she says it in passion, which we know we can’t trust with her. What seems to actually seal the deal for her is knowledge from Dolabella that Caesar will have her marched through the streets as part of his triumphant parade. She can’t bear this indignity.
Cleopatra has poisonous snakes smuggled in to her in a basket of figs. She proclaims she will go to meet her husband, but as she takes the asp (a kind of snake) to her breast, she wishes the snake could call out against Caesar as an "ass unpolicied," meaning one outdone in craftiness in the contest against her. She dies with her pride intact, thinking of joining Antony, but also of having defeated Caesar by robbing him of having conquered her. Caesar finds her, and says she’ll be buried next to Antony, letting the famous pair be together in death. His army will solemnly attend the funeral, and then head back to Rome to finish up this empire business they started.