Get away from it all at one of these high-altitude hideaways.

“The mountains are calling, and I must go,” said the author and wilderness enthusiast Mr John Muir some years ago. He’s not the only one to have found physical release and spiritual succour up there, where the air – and the vista – is rarefied. Everyone from authors to film-makers to adventurers has sought peak inspiration, and, thanks to a new wave of luxurious mountain retreats, you can follow in their tech-booted footsteps. Whichever eyrie you opt for – the intense wilderness of Chilean Patagonia, say, or the splendour of the Indian Himalayas – these six retreats with their stupendous backdrops will transport you to that higher plane where troubles are jettisoned and the mind is comprehensively cleared.

When it opened in 2012, at the head of a remote glacial valley on the shores of Lake Wanaka in New Zealand’s Southern Alps, Minaret Station soon attracted a high-flying crowd. The only way to get here is by boat or helicopter. Once you’re in, you’ve got 50,000 acres to yourself for back-country heli-skiing, heli-hiking, fishing and hunting. The chopper is on hand to fly you further afield should you fancy an overnight camping trip in Fjordland National Park or on Stewart Island, which retains traces of 200 million-year-old forest from the original supercontinent, Gondwana. Family owned, the lodge boasts all the home comforts despite its splendid isolation. Plus, each cabin has an outdoor hot tub.

What to take: A GoPro camera with a mount to fix it to the helicopter skids. This is a once-in-a-lifetime experience that deserves to be recorded.

What to do: Lunch at Minaret’s Mountain Kitchen restaurant costs £586 ($841) per person, but this includes a return chopper flight from Queenstown or Wanaka, a perfect little day trip.

Who to call: Scott Dunn offers a 10-night trip touring the luxury lodges of South Island, with two nights at Minaret, from £6,000 ($8,617) per person, excluding flights.

Novelist Mr Ian McEwan found “a distinguished and unforgettable blend of beauty and adventure” at 360° Leti, a lodge set on a vertiginous plateau 8,000ft up in India’s Kumaon Himalayas. Three days here in the mountains may be worth three years of therapy (tellingly, the lodge was built by an Indian psychoanalyst). 360° Leti, designed by Mumbai architect Mr Bijoy Jain, comprises standalone suites in glass, teak and slate glistening with silver mica. Sunken outdoor fire pits keep you warm at night, along with wood-burning stoves and sheepskin rugs. There is very little human habitation nearby, apart from the deliciously named hamlet of Capri. When night falls and the embers die out, the only light is from the moon and the Milky Way.

What to take: A yoga mat, to perform your sun salutations in the shadow of the sacred peak of Nanda Devi.

What to do: Power down every attempt to connect with the outside world.

Who to call: Book via Cazenove + Loyd and you can take over the whole lodge, which sleeps 16. The company will bring in a private yoga instructor for daily instruction. From £13,000 ($18,665) for five nights, excluding flights.

To journey across the yawning valleys of Chilean Patagonia is to feel as if you are living through the planet’s formation. Mountains are still being carved by the push and pull of tectonic plates in this Andean ridge. Bolts of cobalt run through the glaciers. In Torres del Paine National Park, the intensity of this wilderness is at its most dramatic as high winds whistle through the jagged granite peaks and rocky towers. And just as the horizontal rain can drive through these craggy corridors, so the skies can clear in seconds to reveal the Explora Patagonia. The hotel, as luxurious as it is original, stands like an eccentric, yet contemporary vision of modernist style on the shores of Lake Pehoé.

What to take: Riding chaps. Patagonia’s gauchos can spend hours in the saddle. It’s only polite to keep up.

What to do: Walk as hard and high as you can. The hotel has experienced English-speaking guides who can devise challenging treks according to your ability.

Who to call: Mr Luke Errington at Swoop Patagonia knows this territory well. His company offers a four-night stay from £3,400 ($4,882) per person, including internal flights from Santiago.

Driving the five hours from Bhutan’s international airport to the remote valley of Punakha means traversing mountain passes in excess of 12,000ft. The air is thin. The Himalayas glisten. Local farmers wear knee-length ghos (wraparound robes), revealing sharp white cuffs and dark socks pulled up to their knees. Theatre abounds in Bhutan, in rituals, drum beats and Panavision backdrops. It is cinematic overload, with Uma Punakha, a contemporary 11-room lodge on a hillside above the Mo Chu river, providing retreat-like respite. The combination works: morning yoga, a healthy juice, followed by a (benign) assault to the senses the moment you step out into one of the last bastions of high Himalayan culture.

What to take: A Seek Thermal camera, which can be plugged into an iPhone, to capture yetis at night. The camera shoots in infrared.

What to do: Visit the Temple of the Divine Madman. Wall paintings depict the curious antics of Lama Drukpa Kunley, who was best known for sticking his manhood into the mouths of demons in order to defeat them. Don’t try this at home.

Who to call: Mr Phil Bowen of Guides Of Bhutan is the man to call for any Bhutan expedition. He mixes up activity (mountain biking, hiking, rafting) with dashes of luxury. Minimum seven-night trips cost from £2,750 ($3,948) per person, excluding flights.

The road to Kasbah du Toubkal in Morocco’s High Atlas Mountains passes by Kasbah Tamadot, Sir Richard Branson’s mountain fiefdom at the mouth of the same valley. Press on past this luxury lure, for at the head of this orchard-studded vale lies a bohemian castle fit for Ms Talitha Getty. The kasbah sits on a rocky outcrop in the shadow of Jebel Toubkal, which, at 4,167m, is North Africa’s highest mountain. It was here, in this snow-dusted cradle, that Mr Jean-Jacques Annaud shot Seven Years In Tibet (1997). Kasbah du Toubkal is owned by two British brothers and is run entirely by Berbers. They cook heart-warming tagines like their mothers taught them, served on open terraces where the braying of mules replaces the taxi horns of Marrakech (a 90-minute drive away).

What to take: A wool djellaba, which you can buy in the souks of Marrakech, to keep you warm as you dine al fresco (Moroccan nights are cold).

What to do: Add on a two-day trek, staying overnight at the kasbah’s two-bedroom satellite, Toubkal Lodge.

Who to call: Morocco specialist Lawrence Of Morocco offers a four-night trip from £495 ($711) per person, excluding flights.

Gstaad in Switzerland may have made cinematic history in 1967 when Mr Gunter Sachs and his wife Ms Brigitte Bardot slalomed down the slopes, but, let’s be honest, St Moritz, where Badrutt’s Palace is located, has better skiing, more reliable snow and even boasts polo on the ice. There is a hint of The Grand Budapest Hotel in the merry rapport the hotel’s veteran retainers have with their regular clientele. This is what gives Badrutt’s its character, along with the sweep of a sable coat down its 120-year-old corridors. It’s not cheap, but it is off-the-charts glamorous and situated in a Swiss valley that’s so neat and tidy, even the horse manure is plaited.

What to take: A credit card with no daily limit.

What to do: Eat at Chesa Veglia, a 1658 farmhouse that has been converted into a restaurant. It serves exceptional chateaubriand and blinis loaded with Iranian caviar.

Who to call: Ms Danielle Stynes is the key to the Swiss Alps. Her company SwisSkiSafari can get you all the toys you need, including helicopters, and grant you access to private mountain clubs.