more than 2000 years old.

Depends on which section. Many of them were built during the Ming dynasty (1500s) and some even earlier. Also, many sections are going or have undergone restoration projects which really just turn them into uninteresting tourist traps because they build over any semblance of the walls crumbling character and basically make it look brand new. The wall closest to Beijing is like that. I hiked on Simatai which was fantastic because at the time, in 2008, it had been untouched. It was disastrous and completely falling apart, and dangerous to hike on, but totally worth it. They started a restoration project in 2010 that will, no doubt, make it look sparkling and brand new and instead of preserving what is still there, they will ruin that sense of antiquity that it had...