From conquistadors to criminals, Patagonia has long lured the restless of spirit. Ever since Ferdinand Magellan curved around the crinkled coast of this vast and sparsely populated swathe of South America in the early 16th century, during what would become the first circumnavigation of the world, people have tried to make their mark on Patagonia. His voyage gave the region its Magellanic penguin and crucially, the Strait of Magellan, which became a key shipping route between the Atlantic and Pacific, before the creation of the Panama Canal. The Portuguese explorer was also the first to discover Tierra del Humo – the "Land of Smoke" – after seeing fumes rising along the coast from the burning fires of indigenous people.
The region was later renamed Tierra del Fuego (Land of Fire), after Magellan's king, Charles V of Spain, noted that where there's smoke, there had to be fire. The name Patagonia is said to derive from Magellan's description of the indigenous people as patagónes, or giants. English sailor Francis Drake went one further when he became the first man to anchor off the island of Cape Horn in the Golden Hinde, and Sarmiento de Gamboa established the first strategic settlement of Rey Don Felipe in 1584 – which ultimately failed and was later renamed Puerta del Hambre (Port Famine).
Charles Darwin's voyage on HMS Beagle during the 18th century passed by Patagonia, where he noted the area's distinct geology and wildlife – which today ranges from pumas and penguins to llama-like guanacos and rheas, a relative of the ostrich.
Infamous bandits Butch Cassidy and The Sundance Kid also sought refuge in the plains and pampas of Patagonia. In 1901, the pair fled to Cholila to purchase a log cabin and a 15,000-acre estate, where they lived for five years until the law began to catch up with them.
In pictures: Patagonia
In pictures: Patagonia
Ushuaia, the southernmost city in the world and a starting point for Antarctic exploration
One of many Welsh tea rooms (Rex)
In Chile's Los Lagos region, Chiloé is an archipelago of 30 Pacific islands
Take to horseback You'll get to ride with the gauchos - or huasos, as they are known in Chile
Perito Moreno glacier
Sharp focus: El Chaltén in Argentine Patagonia
Travel writers too, have been seduced by the region's stark wilderness, documented in Paul Theroux's train-based 1979 epic The Old Patagonian Express and Bruce Chatwin's episodic In Patagonia. This month marks 40 years since Chatwin first departed for South America's southern limit, making his book an even more ideal companion to any Patagonian adventure.
While many have tried to stake a claim to this wild expanse, its geography and climate have resisted being easily mastered. Definitions on what constitutes Patagonia vary, but the most commonly agreed upon definition marks it as south of the Río Colorado in Argentina and the Río Biobío in Chile, right down to the continent's southern tip. The Andes form a natural border between the Argentinian and Chilean portions, bounded by the Atlantic to the east, the Pacific in the west and the Tierra del Fuego archipelago in the south as it reaches towards Antarctica.
Largely speaking, the Argentinian side is made up of rolling flat pampas, dotted with estancias (farms), that rise most dramatically around the cordillera (mountains) near El Chaltén, part of the dramatic Los Glaciares National Park (losglaciares.com; admission A$215/£16). In Chile, the landscape is a mass of fjords, glaciers and peaks, which converge most powerfully in Torres del Paine National Park (conaf.cl; admission C$18,000/£19).
Both sides have a lake district in the north, whose water-based activities and volcanoes offer yet more opportunities for adrenalin enthusiasts. Culturally, the two sides share more of a common identity than they do with the citizens of their respective capitals in Buenos Aires and Santiago. There's even a Patagonian flag – marked by the Southern Cross, which defines the clear, unpolluted skies above this great wilderness.
The weather here is unpredictable, but generally speaking, the peak season runs from October to March, with September to April providing quieter shoulder seasons.
I travelled with the specialist operator, Swoop Patagonia (0117 369 0196; swoop-patagonia .co.uk), which can arrange 11-day independent itineraries from £1,240 per person, excluding flights. Its new "Inspirational Itineraries" offer a number of suggested starting points (bit.ly/SwoopInspiration).
Other tour operators offering trips to Patagonia include Journey Latin America (020 3432 9275; journeylatinamerica.co.uk), Tucan Travel (0800 804 8435; tucantravel.co.uk) and Explore (01252 884 223; explore.co.uk). For more tour operators and information, see lata.org.
The towering peaks and glaciers of Torres del Paine National Park are among the most visited places in Chilean Patagonia.
Most people come here to tackle the main mountain range – known as Las Torres (the Towers) – via either the W-Trek, which links five key points in the park, or the longer and more challenging Circuit. Chile Nativo (00 56 2 2717 5961; chilenativo.travel) offers a five-day W-Trek from US$1,595 (£997) per person and a seven-day Circuit from US$1,995 (£1,246) per person, including camping or accommodation in mountain huts, guiding, meals and transfers.
Alternatively, take to horseback. You'll get to ride with the gauchos – or huasos, as they are known in Chile – and sleep at Estancia Tercera Barranca (00 56 61 412 654; bagualesgroup.com), a beautiful working farm. Doubles from US$228 (£143), including breakfast; full-day horse-riding from US$45 (£28) per person.
If you want to see the park on a lighter, more luxurious itinerary, base yourself at Remota in Puerto Natales (00 56 2 2387 1500; remotahotel.com), which offers all-inclusive, three-night stays with excursions and transfers from US$1,950 (£1,219) per person.
Ice, ice baby
The sheer spectacle of standing beneath a towering wall of ice, fractured into a thousand glassy shards, is worth going out of your way for. There are hundreds of glaciers dotted throughout Patagonia – remnants of when the entire region was submerged during the last Ice Age.
One of the most accessible is Perito Moreno in Argentina's Los Glaciares National Park. The gateway to this natural marvel is the charming town of El Calafate, where Kau Kaleshen (00 54 290 249 1188; losglaciares.com/kaukaleshen), an atmospheric casa de té (tea house) and hotel, has B&B doubles from US$80 (£50) and day trips to the glacier from A$290 (£21) per person, excluding entrance to the national park (A$215/ £16pp).
Land of fire
The Tierra del Fuego archipelago fans out either side of the border, at the remote southern tip of Patagonia. On the Argentinian side of the main island, Isla Grande, you'll find Ushuaia (left), the southernmost city in the world and a starting point for Antarctic exploration. On a hill overlooking the bay is the new Hotel Arakur (00 54 2901 44 2900; arakur.com), which offers open-air Jacuzzis and a private reserve with free guided walks. Doubles from US$267 (£167), including breakfast.
Down below, the port of Ushuaia is the starting point for cruises along the Beagle Channel to the outer islands of Tierra del Fuego and Cape Horn. A three-night journey on the MV Stella Australis, to see glaciers, penguins and swirling, leaden seas circled by storm petrels, gives an insight into what Ferdinand Magellan and other 16th-century sailors encountered while traversing the waters at the "End of the Earth".
For modern-day travellers, the journey is infinitely more luxurious, with smart cabins, all drinks and three-course meals included from US$1,486 (£929) per person (00 54 11 5199 6697; australis.com).
If you are arriving from Chile, it also runs trips from Punta Arenas, with departures until late March/ early April.
The northern lake districts on either side of the border offer space for adventure enthusiasts to climb volcanoes, go white-water rafting, hike in national parks, or gaze out at glistening, glacier-fed lakes. In Argentina, Estancia Peuma Hue (00 54 9 2944 50 1030; peuma-hue.com) is a great base, 25 minutes outside the main hub of Bariloche, on the edge of Lake Gutiérrez. Nightly packages start at US$315 (£210) per person, with meals and excursions such as fishing, kayaking and trekking.
In Chile's Los Lagos region, Chiloé is an archipelago of 30 Pacific islands. The locals, known as Chilotés, worked across southern Patagonia as peons (farm workers) and used their carpentry skills to craft many of the low-rise, wooden buildings. In Chiloé itself, the origin of Patagonia's distinct architecture can been seen in the houses dotted around the islands. Austral Adventures (00 56 65 625 977; austral-adventures.com) offers day tours from US$85 (£53) per person.
For a luxury stay, consider Tierra Chiloé (00 56 2 2207 8861; tierrachiloe.com), which has two-night, all-inclusive packages from US$1,150 (£767) per person, with transfers and excursions.
As well as explorers, runaways and writers, another wave of settlers arrived, in the 19th century. Mostly north Europeans, these immigrants were searching for land in a vast and inhospitable region, of which they knew little. In the Chilean Lake District, you can find a thriving German population.
Around Torres del Paine, surnames hint at the area's Croatian input. But there's one group that will come into the spotlight next year, as 2015 marks the 150th anniversary of the first Welsh settlers' arrival in Argentina, moving from Puerto Madryn through Chubut province to places such as Trevelin, Trelew and Gaiman – where you can visit one of many Welsh tea rooms, such as Ty Te Caerdydd, for unlimited tea and cakes (A$180/ £13; 00 54 280 449 1510).
Today, there are 50,000 descendants living in Patagonia – many of whom still speak Welsh – who will help celebrate the anniversary through next year (patagonia2015.com).
For more details on the Welsh in Patagonia, see Project Hiraeth (project-hiraeth.com).
The international gateways to Patagonia are the Argentinian and Chilean capitals. British Airways (0844 493 0787; ba.com) flies from Heathrow to Buenos Aires. No airline flies direct from the UK to Santiago in Chile, but connections are available on LAN (0800 026 0728; lan.com) and Iberia via Madrid, on TAM via Sao Paulo in Brazil and American Airlines (0844 499 7300; aa.com) via Miami.
The writer travelled with KLM (020 7660 0293; klm.com), which offers open-jaw tickets from many UK airports via Amsterdam, into Buenos Aires, out of Santiago, from £885. Internal flights are available on Aerolineas Argentinas (0800 0969 747; aerolineas.com.ar) and LAN.
Buses connect the main cities, and 4x4 car hire is also widely used, with road trips popular along the Ruta 40 (ruta40.gov.ar).
While Chilean pesos comprise a solid currency, in Argentina change at the preferable "blue" rate (bit.ly/BluePeso).