YOSEMITE NATIONAL PARK, Calif. » A pair of Americans on Wednesday completed what had long been considered the world’s most difficult rock climb, using only their hands and feet to conquer a 3,000-foot vertical wall on El Capitan, the forbidding granite pedestal in Yosemite National Park that has beckoned adventurers for more than half a century.

Tommy Caldwell and Kevin Jorgeson became the first to "free-climb" the rock formation’s Dawn Wall, a feat that many had considered impossible. They used ropes and safety harnesses to catch them in case of a fall, but relied entirely on their own strength and dexterity to ascend by grasping cracks as thin as razor blades and as small as dimes.

The effort took weeks, as the two dealt with constant falls and injuries. But their success completes a years-long dream that bordered on obsession for the men.

The trek up the world’s largest granite monolith began Dec. 27. Caldwell and Jorgeson lived on the wall itself. They ate and slept in tents fastened to the rock thousands of feet above the ground and battled painful cuts to their fingertips much of the way.

Free-climbers do not pull themselves up with cables or use chisels to carve out handholds. Instead, they climb inch by inch, wedging their fingertips and feet into tiny crevices or gripping sharp, thin projections of rock. In photographs, the two appeared at times like Spider-Man, with arms and legs splayed across the pale rock that has been described as smooth as a bedroom wall.

Both men needed to take rest days to wait for their skin to heal. They used tape and even superglue to help with the process. At one point, Caldwell set an alarm to wake him every few hours to apply a special lotion to his throbbing hands.

They also took physical punishment when their grip would slip, pitching them into long, swinging falls that left them bouncing off the rock face. The tumbles, which they called "taking a whipper," ended in startling jolts from their safety ropes.

Caldwell and Jorgeson had help from a team of supporters who brought food and supplies and shot video of the adventure.

The 36-year-old Caldwell and 30-year-old Jorgeson ate canned peaches and occasionally sipped whiskey. They watched their urine evaporate into thin, dry air and handed toilet sacks, called "wag bags," to helpers who disposed of them.

There are about 100 routes up the rock known among climbers as "El Cap," and many have made it to the top, the first in 1958. Even the Dawn Wall had been scaled. Warren Harding and Dean Caldwell (no relation to Tommy) made it up in 1970, using climbing ropes and countless rivets over 27 days.

No one, however, had ever made it to the 3,000-foot summit in one continuous free-climb — until now.

The pioneering ascent comes as a result of five years of training and failed attempts for both Caldwell and Jorgeson. They only got about a third of the way up in 2010 when they were turned back by storms. A year later, Jorgeson fell and broke an ankle in another attempt. Since then, each has spent time on the big, blank rock practicing and mapping out strategy.

On this try, as the world watched and followed on Facebook and Twitter, Jorgeson was stalled by a lower section that took 11 attempts over the course of seven days.

"As disappointing as this is, I’m learning new levels of patience, perseverance and desire," Jorgeson posted online. "I’m not giving up. I will rest. I will try again. I will succeed."

Caldwell, of Estes Park, Colorado, is no stranger to El Cap. He has free-climbed 11 different routes and was the first to make such ascents of the Dihedral Wall and West Buttress. He was the third to free-climb the Nose on El Cap. He also made his way up a challenging El Capitan route in fewer than 24 hours — becoming only the second person to do so — only months after accidentally severing his left index finger with a table saw in 2001.

In 2000, Caldwell and three other climbers went to the former Soviet republic of Kyrgyzstan to scale the towering rock walls of its southern mountains. Seventeen days in, they were captured by the Islamic Movement of Uzbekistan. Caldwell shoved a guard over a cliff, and the climbers fled, eventually reaching a Kyrgyz army outpost. The guard survived the fall.

Jorgeson, of Santa Rosa, California, has an impressive list of climbs in the U.S., Europe and South Africa. He works as a climbing instructor and co-founded an advocacy group for the climbers.

Still, the difficulty of the climb wasn’t a surprise.

John Long, the first person to climb up El Capitan in one day in 1975, said recently of Caldwell and Jorgeson’s free-climb that it was almost "inconceivable that anyone could do something that continuously difficult."