What happens in Canto XX of Dante's Inferno?

Canto XX
Presumably Pope Nicholas III was still kicking his feet furiously as Dante and Virgil took their leave of him and the other Simonists in the third pouch of Circle Eight. The poets have crossed the bridge (Virgil physically carrying Dante), and have stepped carefully down the sharp incline into pouch four.
A horrific scene unfolds before them. Lines of sinners march quietly. Upon closer inspection, Dante sees that their heads face backwards; the shades must proceed slowly, as they cannot see what is in front of them. Their sorrow is so great that the tears roll down their backsides:

“Wondrously each one seemed to be distorted
From chin to the beginning of the chest;
For tow'rds the reins the countenance was turned,
And backward it behoved them to advance,
As to look forward had been taken from them.”

Unlike the Simonists for whom Dante had no pity, the state of agony of this group of sinners moves the poet to tears:

“As God may let thee, Reader, gather fruit
From this thy reading, think now for thyself
How I could ever keep my face unmoistened,
When our own image near me I beheld
Distorted so, the weeping of the eyes
Along the fissure bathed the hinder parts.
Truly I wept, leaning upon a peak
Of the hard crag…”

Virgil, however, feels no such pity. He chastises Dante for his emotion:

“Art thou, too, of the other fools?
Here pity lives when it is wholly dead;
Who is a greater reprobate than he
Who feels compassion at the doom divine?
Lift up, lift up thy head, and see for whom
Opened the earth before the Thebans' eyes…”

Virgil points out several of their number. There is the cowardly King Amphiaraus, who, learning of his impending defeat, tried to hide. Also among this number is the gender conflicted Tiresias, who changed his sex from male to female and back again; Virgil continues, naming the diviner Aruns, the man who predicted Rome’s civil war and its outcome:

'Whither rushest thou,
Amphiaraus? Why dost leave the war?'
And downward ceased he not to fall amain
As far as Minos, who lays hold on all.
See, he has made a bosom of his shoulders!
Because he wished to see too far before him
Behind he looks, and backward goes his way:
Behold Tiresias, who his semblance changed,
When from a male a female he became,
His members being all of them transformed;
And afterwards was forced to strike once more
The two entangled serpents with his rod,
Ere he could have again his manly plumes.
That Aruns is, who backs the other's belly,
Who in the hills of Luni, there where grubs
The Carrarese who houses underneath,
Among the marbles white a cavern had
For his abode; whence to behold the stars
And sea, the view was not cut off from him."

Lastly, Virgil points out a woman who in life had been the sorceress Manto, whose long, dirty hair now covers her breasts:

“And she there, who is covering up her breasts,
Which thou beholdest not, with loosened tresses,
And on that side has all the hairy skin,
Was Manto, who made quest through many lands…”

The sight of Manto reminds Virgil of his homeland, Mantua (the town named for the witch). He tells Dante about Manto’s history. As a young girl, Manto had to leave Thebes after her father was killed; she finally found a place to live near a lake named Benaco. The chief attraction to this marshy, smelly area was its relative safety from the wars that raged not far away. Other people soon came to the same conclusion, and joined Manto in her safer place, eventually naming the town after her, “Mantua.”
While Dante has not said a word, nor are there any indications that Dante disbelieves his mentor, Virgil nonetheless challenges Dante, daring him, in essence, to call him a liar:

“I caution thee, if e'er thou hearest
Originate my city otherwise,
No falsehood may the verity defraud."

Whether he actually doubts Virgil, Dante replies that he indeed believes the elder poets story:

"My Master, thy discourses are
To me so certain, and so take my faith,
That unto me the rest would be spent coals.
But tell me of the people who are passing,
If any one note-worthy thou beholdest,
For only unto that my mind reverts."

Dante then asks for Virgil’s help in identifying more of the sinners in the fourth pouch. Virgil complies, pointing out Calchas, who oversaw the sacrifice of Iphigenia (in “The Aeneid”) and was an interpreter of entrails of the enemy dead. He identifies two astrologers, Michael Scot and Guido Bonatti, and the soothsayer Asdente.
There is nothing more to be said here. Virgil tells Dante it is time to move on as the hour grows late.