At 29,028 feet, Mount Everest in Asia's Himalayan mountain range is the tallest mountain on Earth. Someone standing on the peak has an unblocked view of the horizon in all directions. Below are the countries of Nepal and Tibet, and 100 miles away is Darjeeling, India, where the first expeditions to climb Everest began.

Only fourteen other peaks in the world even come close to Everest's height, and most of them are also in the Himalayas. These peaks are known as "the Eights" because they are all more than 26,240 feet—or 8,000 meters— high. Their bad weather, heavy snow, and glacial ice present formidable challenges to even the best mountaineers. But more importantly, their altitudes are so high that no human being can survive on them for very long because, above 8,000 meters, there is not enough oxygen in the air to...