During Odysseus adventure, the next land Odysseus's crew and him visited had cyclopes there.
Reasoning With The Beast
Odysseus and his 12 best fighters went to the Cyclopes' mainland after seeing a cyclopes in a cave alone.
The Eye Escape
While Odysseus was explaining how "we are survivors, theses good men and I." The cyclopes took no pity and grabbed Odysseus fighters, killed them then ate them. After the repeatedly incident with the cyclopes, Odysseus and the rest of his fighters took a big piece of wood, sharpened it and hid it in the cave.
What is next
Odysseus gave the cyclopes some wine to try to reason with them. Also Odysseus wants to make an arrangement to get back home.
Odysseus and his crew attempt to escape by using a spike and started clawing his face. They managed to take out his eye.
After Odysseus and his crew fought hard and used their boat to escape the cyclopes, they started to sail to Aeolia.