Both Tiberius and Caligula were disliked by the social elite, who wrote the history books and biographies that we draw our information from. This means that our sources (and their sources!) are known to be hostile and should not be taken at face value.

The major sources for this period are Cassius Dio, Tacitus and Suetonius. The main source for this topic is Suetonius, a biographer and something of a gossip. He is not considered to be a particularly strong source, in part because his purpose was not to record history but to display and explain character. Still, Suetonius' book The Twelve Caesars is well worth reading, both for information (provided you are careful with it) and for pleasure. Take this as evidence of the kind of sexual pleasures Tiberius and Caligula were accused of, rather than of the kind of sexual pleasures they actually engaged in.

On Tiberius, he says:

Being invited to dinner by Cestius Gallus, a lecherous old spendthrift whom Augustus had ignominiously removed from the Senate and whom he had himself reprimanded only a few days previously, Tiberius accepted on condition that the dinner should follow Gallus' usual routine, and that the waitresses should be naked. ... On retiring to Capreae he made himself a private sporting-house, where sexual extravagances were practiced for his secret pleasure. Bevies of girls and young men, whom he had collected from all over the Empire as adepts in unusual practices, and known as spintriae, would copulate before him in groups of three, to excite his waning passions. A number of small rooms were furnished with the most indecent pictures and statuary obtainable, also certain erotic manuals from Elephantis in Egypt; the inmates of the establishment would know from these exactly what was expected of them. He furthermore devised little nooks of lechery in the woods and glades of the island, and had boys and girls dressed up as Pans and nymphs prostituting themselves in front of caverns or grottoes so that the island was now openly and generally called 'Caprineum' [a play on the word for 'goat'].

Some aspects of his criminal obscenity are almost too vile to discuss, much less believe. Imagine training little boys, whom he called his 'minnows', to chase him while he went swimming and get between his legs to lick and nibble him. Or letting babies not yet weaned from their mother's breast to such at his breast or groin - such a filthy old man he had become! Then there was a painting by Parrhasius, which had been bequeathed to him on condition that, if he did not like the subject, he could have 10,000 gold pieces instead. Tiberius not only preferred to keep the picture but hung it in his bedroom. It showed Atalanta performing fellatio with Meleager.

The story goes that once, while sacrificing, he took an erotic fancy to the acolyte who carried the incense casket, and could hardly wait for the ceremony to end before hurrying him and his brother, the sacred trumpeter, out of the temple and indecently assaulting them both. When they jointly protested at this disgusting behaviour he had their legs broken.

What nasty tricks he used to play on women, even those of high rank, is clearly seen in the case of Mallonia whom he summoned to his bed. She showed such an invincible repugnance to complying with his lusts that he set informers on her track and during her very trial continued to shout: 'Are you sorry?' Finally she left the court and went home; there she stabbed herself to death after a violent tirade against 'that filthy-mouthed, hairy, stinking old man'.

On Caligula:

It was his habit to commit incest with each of his three sisters and, at large banquets when his wife reclined above him, placed them all in turn below him. They say that he ravished his sister Drusilla before he came of age: their grandmother Antonia, at whose house they were both staying, caught them in bed together. Later, he took Drusilla from her husband, the former Consul Lucius Cassius Longinus, openly treating her as his lawfully married wife ...

It would be hard to say whether the way he got married, the way he dissolved his marriages, or the way he behaved as a husband was the more disgraceful. He attended the wedding ceremony of Gaius Piso and Livia Orestilla, but had the bride carried off to his own home. After a few days, however, he divorced her, and two years later banished her, suspecting that she had returned to Piso in the interval. According to one account he told Piso, who was reclining opposite him at the wedding feast: 'Hands off my wife!' and abducted her from the table at once; and announced the next day that he had taken a wife in the style of Romulus and Augustus. Then he suddenly sent for Lollia Paulina, wife of Gaius Memmius, a Governor of consular rank, from his province, because somebody has remarked that her grandmother was once a famous beauty; but soon discarded her, forbidding her ever again to sleep with another man. Caesonia was neither young nor beautiful, and had three daughters by a former husband, besides being recklessly extravagant and utterly promiscuous; yet he loved her with a passionate faithfulness ... For his friends he even paraded her naked; but would not allow her the dignified title of 'wife' until she had borne him a child, whereupon he announced the marriage and the birth simultaneously ...

He had not the slightest regard for chastity, either his own or others', and was accused of homosexual relations, both active and passive, with Marcus Lepidus, also Mnester the comedian, and various foreign hostages; moreover a young man of consular family, Valerius Catullus, revealed publicly that he had buggered the Emperor, and quite worn himself out in the process. Besides incest with his sisters, and a notorious passion for the prostitute Pyrallis, he made advances to almost every woman of rank in Rome; after inviting a selection of them to dinner with their husbands he would slowly and carefully examine each in turn while they passed his couch, as a purchaser might assess the value of a slave, and even stretch out his hand and lift up the chin of any woman who kept her eyes modestly cast down. Then, whenever he felt so inclined, he would send for whoever pleased him best, and leave the banquet in her company. A little later he would return, showing obvious signs of what he had been about, and openly discuss his bed-fellow in detail, dwelling on her good and bad physical points and commenting on her sexual performance. To some of these unfortunates, he issued, and publicly registered, divorces in the names of their absent husbands.

Addition question: were the acts intentionally performed with other powerful figures as a form of shared blackmail similar to modern politics and scandals?