What happens in Canto XVI of Dante's Inferno?

Canto XVI
Dante’s former mentor, Brunetto Latini, has made a hasty retreat. The poets continue their descent into Hell. The way becomes more steep and the river Phlegethon narrows. Dante hears a distant roar, like the humming of an enormous beehive. Before he can ask what causes the sound, he spies three whirling shades approaching.
The three recognize Dante as a fellow Florentine and call out, asking him to tarry:

"Stop, thou; for by thy garb to us thou seemest
To be some one of our depraved city."

Dante pauses, horrified by their scarred and melting flesh. Dante must have looked hesitant about listening to the sinners, because Virgil urges him to listen and reply:

"Now wait,"
He said; "to these we should be courteous.
And if it were not for the fire that darts
The nature of this region, I should say
That haste were more becoming thee than them."

However, before the trio speaks again, they act very oddly; they link arms and form a wheel-shape, spinning as they come closer to the travelers. Apparently, they keep hold of each other so that no one among them can harm another. As they whirl, Dante gets a glimpse of each of their faces:

"As soon as we stood still, they recommenced
The old refrain, and when they overtook us,
Formed of themselves a wheel, all three of them.
As champions stripped and oiled are wont to do,
Watching for their advantage and their hold,
Before they come to blows and thrusts between them,
Thus, wheeling round, did every one his visage
Direct to me, so that in opposite wise
His neck and feet continual journey made."

After asking, as all the denizens of Hell do, how a living man can be here, the shade reveals that he is Jacopo Rusticucci. Rusticucci identifies his companions as Guidoguerra and Tegghiaio Aldobrandi. Jacopo Rusticucci, as well as the two others, had been Guelphs in Florence when they were alive. What Rusticucci most wants to know from Dante is the state of affairs in present-day Florence. He also makes sure Dante understands that his “savage wife” is responsible for his behavior as a sodomite, and thus his punishment in Hell’s Seventh Circle:

"He in whose footprints thou dost see me treading,
Naked and skinless though he now may go,
Was of a greater rank than thou dost think;
He was the grandson of the good Gualdrada;
His name was Guidoguerra, and in life
Much did he with his wisdom and his sword.
The other, who close by me treads the sand,
Tegghiaio Aldobrandi is, whose fame
Above there in the world should welcome be.
And I, who with them on the cross am placed,
Jacopo Rusticucci was; and truly
My savage wife, more than aught else, doth harm me."

Dante immediately recognizes the names and is almost overcome by compassion for the burning souls. He begins to move from the relative safety of the cooler banks of the Phlegethon, but quickly realizes the foolishness of doing so. From a distance, Dante assures Rusticucci how much he esteemed all three of them in life and that when he returns to the land of the living, he will make sure their names are kept alive:

"Sorrow and not disdain
Did your condition fix within me so,
That tardily it wholly is stripped off,
As soon as this my Lord said unto me
Words, on account of which I thought within me
That people such as you are were approaching.
I of your city am; and evermore
Your labours and your honourable names
I with affection have retraced and heard.
I leave the gall, and go for the sweet fruits
Promised to me by the veracious Leader;
But to the centre first I needs must plunge."

Before taking their leave, Rusticucci asks Dante to tell him whether Florence has become more corrupt due to the influence of Guiglielmo Borsiere, one of the burning circle of three but a recent resident in Hell. Dante tells them that Florence has suffered since Rusticucci’s abscence:

"The new inhabitants and the sudden gains,
Pride and extravagance have in thee engendered,
Florence, so that thou weep'st thereat already!"
In this wise I exclaimed with face uplifted;
And the three, taking that for my reply,
Looked at each other, as one looks at truth."

With this information, the horrific threesome splits from one another. A final plea to Dante is made that he remember their names to the living world, then all three run speedily away from Dante’s sight and hearing.
The poets continue on; the roar Dante heard earlier becomes louder. The river has become an enormous waterfall, one that reminds Dante of a river in Florence, the Acquacheta, which feeds into the Apennines.
The power of this waterfall is terrifying. But what Virgil does next is even more frightening. The elder poet tells Dante to remove the rope-like belt from around his waist. Virgil tosses the rope into the churning waters below.
Virgil tells his charge to wait and see what happens:

"Soon there will upward come
What I await; and what thy thought is dreaming
Must soon reveal itself unto thy sight."

Soon, Dante sees something caught in the rope’s lasso, something so horrible that he exclaims, but does not tell the reader what exactly he is witnessing, saying only:

“But here I cannot; and, Reader, by the notes
Of this my Comedy to thee I swear,
So may they not be void of lasting favour,
Athwart that dense and darksome atmosphere
I saw a figure swimming upward come,
Marvellous unto every steadfast heart,
Even as he returns who goeth down
Sometimes to clear an anchor, which has grappled
Reef, or aught else that in the sea is hidden,
Who upward stretches, and draws in his feet.”