There's a mountain in Switzerland that's always looking down on you—but don't take it personally. At over 3,000 metres, Piz Nair of the Albula Alps keeps an eye over the Engadine valley in Graubünden. Start in St. Moritz: hop on the funicular (a type of cable railway system) to Corviglia, then ride the cable car to the summit. This alpine peak hosted the 1948 Winter Olympics and still boasts some of the most famous ski runs in the country. The 'Piz Nair Wall' is known for its challenging downhill skiing and events like the 2003 World Championship downhill race. Come summer, the snow clears but the trails stay hot.

Thousands of kilometres away in the Janak section of the Himalayas, Jongsong Peak rises to 7,462 metres. While it's the 57th highest peak in the world, it stands in the shadow of Kangchenjunga—the world's third highest—just 20 kilometres to the south. Unlike Switzerland's ski-friendly slopes, Jongsong is a remote giant, its summit marking the tripoint where India, Nepal and China meet.