(CNN) -- They spent 69 days in the bowels of the earth, 700 meters deep, not knowing if they would survive. For 17 days after the mine in which they were working collapsed, nobody even knew if they were alive. Friday marks the one-year observance of the fateful incident in Chile that trapped 33 miners who were saved in a miraculous rescue that made headlines around the world.

Fame came after the rescue, which faded quicker in their country than abroad, and since then they have traveled to several destinations all-expenses-paid, though many report having money problems.

Four of the miners will observe the anniversary of the event that changed their lives in Washington where an exhibit in their honor is being opened at the Smithsonian Institution.

Mario Sepulveda, one of the miners attending, reflected on the historical significance of the event.

"In spite of our painful experience, it is very important to us that what is being exhibited will show the world what happened," Sepulveda said. He was the second to be rescued from the mine.

Since they were rescued last October, the miners have traveled the world. Edison Pena, the miner whose underground workouts in the darkness garnered attention, ran the New York Marathon less than a month after being rescued.

Pena also appeared on "The Late Show with Dave Letterman" on CBS where he impersonated his idol, Elvis Presley. Then, in January, he was invited as a guest of honor to the Graceland Mansion, in Memphis, Tennessee. Pena had dreamed of visiting the mansion since he became an Elvis fan as a teenager.

In January, the entire group of 33 was honored at Disney World in Orlando, Florida. While there, they served as honorary Grand Marshals of Disney's Main Street U.S.A parade. They spent a full week in Orlando enjoying the attractions.

But at home in Chile celebrity has not been what they expected, according to one of the miners, Jorge Galleguillos.

The good will from their country faded fast, he said.

"They love us more abroad. They congratulate us, they want to touch us and get a blessing from us. That's not the case in Chile. Only a few greet us with affection; many more say hi with envy," Galleguillos said.

A movie about the miners' ordeal is in the works. According to the Hollywood Reporter, producer Mike Medavoy ("Shutter Island", "Black Swan") has snapped up the right to the story and Jose Rivera ("Motorcycle Diaries") has been enlisted to adapt the screenplay.

But at home, relations with the Chilean government are strained. Thirty-one of the 33 miners filed a lawsuit accusing the agency that oversees mining of failing to ensure safety measures.

Carlos Barrios, the 13th miner rescued, says they're not targeting President Sebastian Pinera.

"We're not suing the current president. This has been happening for a long time. This happened during the administrations of other presidents. Why didn't they take a closer look [at the situation]?" Barrios asked.

Hernan de Solminihac, the Chilean mining minister, said his government respects the miners' right to sue.

"As any Chilean citizen, the miners have the freedom and the right to file any lawsuit they wish. They have chosen to do so and our judicial authorities are evaluating the suit," he said.

The miners are seeking the equivalent of $16 million in damages for the collapse of the mine where they were trapped last year in the Chilean Atacama desert. They say their lawsuit isn't about the money, but about raising awareness about the working conditions for miners in their country, which they say, has been neglected for a long time.