Since December 27, Caldwell and Jorgeson have been scaling the 3,000-foot rock formation. Now, it appears the duo will reach the summit on Wednesday or Thursday.
The route Caldwell and Jorgenson are attempting is the notoriously difficult Dawn Wall, more than a half mile high.
There are many routes up El Capitan, but only a handful have been attempted by climbers trying to free climb -- using only their hands and feet -- with ropes designed only to catch them when they fall. And none have successfully conquered El Capitan's Dawn Wall.
Perhaps no route is more challenging than the Dawn Wall, which offers few footholds and may be the most difficult climb in the world. If they succeed, Caldwell and Jorgeson would be the first to successfully free-climb the Dawn Wall, Yosemite National Park officials confirmed.
For Caldwell, it's a dream that has been in the making for several years. An accomplished climber, Caldwell already completed five other routes on El Capitan, according to his bio. But family members say the Dawn Wall route is one that has consumed him.
"He was looking for more of a challenge" said Caldwell's father Mike. "He started going up and repelling down and trying to see if he could see holds that could turn into a climb. Over a two-year period, he probably spent 25-30 days on the wall just looking it over."
Jorgeson, who started climbing competitively as a teenager, didn't know Caldwell until he decided to join him on the climb.
"Kevin called Tommy offering to help with the climb and that's how they met," Mike Caldwell said.
The team attempted an earlier push on the project several years ago, but were shut down due to weather, according to Caldwell's Facebook page.
The anticipation of completing the climb is generating excitement, with family members headed to the mountain. Tommy Caldwell's wife left Colorado Monday headed to Yosemite, and Caldwell's parents are heading that way Tuesday.
The climbers, meanwhile, have expressed the adventure's joys and heartaches through various social media accounts.
Follow their journey on Caldwell
Instagram accounts, Caldwell
Facebook accounts and YouTube