The making of The Odyssey is already becoming the stuff of Hollywood legend.

The arduous, globe-trotting shoot, helmed by director Christopher Nolan, took Matt Damon and the cast to locales around the world Greece, Morocco, Iceland, Scotland and Italy.

“It really felt more like an expedition than a movie,” Damon, who plays Odysseus in the epic adaptation of the ancient Greek myth, tells PEOPLE in this week’s cover story. “And if you were cold and wet, you just turned and you looked and Chris was just as cold and just as wet and going through it.”

Still, no one exhaled when production finally moved to a water tank at Universal Studios in Los Angeles. “Every location was really difficult, but in a really different way,” he says. “We knew we were ending at the water tank in Universal. And nobody said, ‘Well, it’ll probably be easier once we get to it.’”

He continues, “And sure enough, there were these two jet engines, like 737 engines, blowing water on us. It was definitely about as hard as you can make water work in a controlled environment.”

And as production neared its end, scenes got comically intense. “We were laughing at the end because we were shooting some close up raft stuff that was too dangerous to do on the open water. So we’d shot some wides, but we did some stuff on the tank that involved Chris pouring water over my face while I was lying there and I was like, “This is perfect. We’re ending this with water boarding,” Damon laughs.

After being chased by a Cyclops and stuffed into a giant Trojan Horse, could he have any phobias left? “I worked through a lot of them on this one, definitely,” he laughs. “Claustrophobia was one, but I hope I’m on the other side of that one now.”

But in the end, the experience of translating Homer’s tale, estimated to be almost 3,000 years old, became a singular experience.

“You could not look in any direction and not see somebody just giving everything they had for this kind of common project,” Damon says, adding that every Friday, the exhausted cast and crew felt a shared sense of accomplishment after making it through another week.

“I like to say it was a hard shoot, but hard in the right way,” Nolan tells PEOPLE of his all-star cast, which includes Anne Hathaway, Tom Holland, Zendaya and Charlize Theron. Put to the test, “they rose to it magnificently.”

Despite The Odyssey’s physical demands, Damon calls the experience of making the film profound.

“I had such a feeling of gratitude,” he says. “It was the best experience I’ve ever had because everybody on the set was experienced enough to know that the movie required everybody to be completely maxing out and straining against what they thought was possible and what they’d done before.”

The Odyssey is in theaters July 17.