Polyphemus' Cave

Polyphemus' Cave is a cave on an island in the middle of The Sea of Monsters. Polyphemus uses it as a home for himself and the sheep that live with him on his island. He also used it as a prison for Satyrs and anyone else he wanted locked up. Its front door was a boulder, but Annabeth was distracting him by taunting him while she was wearing her magic Yankees cap so that Percy could get into the cave invisible to Polyphemus's view. That made Polyphemus pick up his front door, and throw it in the direction he heard her voice, breaking the boulder.

The Sea of Monsters
In The Sea of Monsters, Grover was taken to this cave after he tricked Polyphemus into thinking Grover was a female Cyclops who wanted to marry him. Grover then pretended to make a wedding dress while really making an Empathy Link with Percy, telling Percy that Polyphemus has got him trapped on his island in The Sea of Monsters and that he needs rescuing but also that he unknowingly found the cure for Thalia's Tree. After Clarisse tried to rescue Grover and take the Golden Fleece back to Camp Half-Blood, she got locked in the cave as well. Percy and Annabeth eventually break in and saved them both from Polyphemus who wants to marry Grover, thinking that Grover is a female Cyclops but realizes that Clarisse is a female person. Polyphemus' cave is full of sheep collector items.