Blindness
What Happens
The story is from the perspective of the cyclops. Quiet and antisocial, he admits he is not handsome and lives peacefully with his goats. He calls himself a philosopher, though one who does not think much, and instead enjoys the sun in his eyes and being able to see the ocean view.
Compare and Contrast to the Odyssey
Compare
Contrast
Odysseus and his men come to the Cyclops. They get him drunk and stab his eye out. All of the stories the Cyclops imagines as punishments to Odysseus for his crimes are actually true. The men are indeed toned from war far from home, eager to return. They only know violence, as it is the one thing they have done repeatedly throughout the Odyssey.
Comparing the Perspectives of the "VILLAINS"
When he returns to his cave, he finds Odysseus and his men, expecting to receive Xenia. The Cyclops, still woozy from the sun for hours, gets thrown in a fit of rage and kills one of his men. Both sides seemingly apologetic, Odysseus gives him wine, which he drinks and then falls asleep because of. When he wakes up, it's to a blinding pain from the spear. The men all flee and the Cyclops is furious and hurt.
Whether his father Poseidon heard him or not, he doesn't know. Later, he bandages his wound and falls under a fever. The fever almost kills him, and though he is blind he sees a vision of Hermes, golden and holding his medicinal symbol of a staff with snakes wound around it.
The story is from a first-person perspective of the Cyclops, and does not highlight Odysseus' life, but instead his own. Instead of Poseidon getting revenge on the men in the story, the Cyclops feels ignored by his father, aimlessly throwing rocks and never getting revenge.
Poseidon comes, shoos him away, and then saves the Cyclops, his son. Though he is still blind, he is alive, and lives the rest of his time tending to his goats and being more polite to the island farmers who would come and bring him gifts and hear his stories.
Though the Cyclops was once violent and held much hate in his heart towards cruel Odysseus and made up "stories" about him (that are actually true in the Odyssey), but never truly killed him, feeling guilty. In the end, the cyclops is grateful that he does not have sight as a distraction and sleeps better with less bloodthirstiness.
There are sirens, fields of the dead, and monsters of the sea (like Scylla and Charybdis). He even is conjured up in the Cyclops' mind that his home is an island with a perfect and loyal wife, waiting for his return.
In the Odyssey, the Cyclops hears his name and says it so that the gods can act revenge on him. In this story, the Cyclops is too infuriated and noisy to hear the actual words of Odysseus.
Scylla was told in a prophecy that in her monster form she would be killed by Odysseus in another riff, "Killing Scylla." Despite being seen as evil, she was actually a fearful and hopeless monster, unable to leave her cave except for occasional food. 
In Madeline Miller's Circe, Circe is simply a woman who does magic, and punishes men accordingly, not because she's evil but because the men are. She is accused, assaulted, and abused yet never seen as the victim until Circe. 
IN SUMMARY
The "villains" of the Odyssey are often pictured poorly for Odysseus' glorification. In reality, they are all sentient beings who are misunderstood and wrongly treated.
Put yourself in the shoes of others before acting against them.