A free wilderness permit (available at any of Yosemite’s Wilderness Centers) is required to camp anywhere in Yosemite’s Wilderness. However, an exception to this rule is made for climbers sleeping off the ground on multi-day routes. However, it is not permitted to sleep at the base of El Capitan, Washington Column, Leaning Tower, Liberty Cap, or any other walls in Yosemite Valley. Camping at the base of the NWF of Half Dome or other backcountry walls is allowed with a valid permit.
All food, drinks, toiletries, and other scented items must be stored properly at all times to protect Yosemite's bears and other wildlife. (Learn more about food storage while climbing.)
Yosemite's wilderness permit system attempts to achieve two goals: limit the number of people in the Yosemite Wilderness to ensure a more pristine wilderness experience, and educate wilderness users how to minimize their impacts while in the wilderness.
As climbing grows in popularity, impacts from the sport increase, and the need for education grows. Currently, the number of climbers and their resulting impacts are not seen as large enough to warrant a permit system, but this question is open to debate.
"Why can't we sleep at the base of El Capitan?" For the same reason visitors can’t just sleep anywhere they want in the park. In order to protect Yosemite while letting people enjoy it, the National Park Service restricts camping to certain areas and limits the number of campsites in those areas. Wherever you camp, minimize your impact; carry out all trash, store your food appropriately, build fires only in legal campsites with established fire rings, bury your human waste at least six inches underground or pack it out, and leave no trace behind.