Christ the Redeemer’s open arms, a cable car ride from a Lapa dance floor.

Rio de Janeiro takes its name from a navigational mistake: Portuguese sailors entering Guanabara Bay in January 1502 believed they had found the mouth of a great river, and named it accordingly. The city itself was founded in 1565 as a fortified outpost against French incursions, and grew slowly until gold and diamonds from Minas Gerais made it colonial Brazil’s most important port; Rio replaced Salvador as the colony’s capital in 1763, and in 1808, fleeing Napoleon’s armies, the entire Portuguese royal court relocated across the Atlantic, briefly making Rio the only European capital ever to sit outside Europe. Christ the Redeemer, raised on Corcovado’s granite peak in 1931 and later named one of the New Seven Wonders of the World, and the Maracanã, built for the 1950 World Cup and rebuilt again for 2014, both belong to a city that has repeatedly built or rebuilt its own icons rather than resting on the last one. Carnival grew up alongside them: the samba schools that now compete in the purpose-built Sambadrome trace back to hillside communities of the 1920s and 1930s, and the parade remains a genuine, year-round civic undertaking rather than a show staged for visitors.

Rio’s geography does as much work as its history. Two granite peaks — Sugarloaf and Corcovado — rise directly from the shoreline, Sugarloaf reached by a cable car system opened in 1912, among the earliest in the world and still running the original route between its two stages. The beaches below are not interchangeable: Copacabana filled with grand hotels from the 1920s onward and still hosts New Year’s Eve fireworks watched by millions on the sand, while Ipanema built its own, quieter mystique a generation later — the woman who inspired “The Girl from Ipanema” in 1962 really did walk past the songwriters’ usual bar table on her way to the sea. Favela neighbourhoods such as Rocinha, Brazil’s largest, grew up on the hillsides between and above the formal city through the twentieth century, and today a resident-led walking tour is one of the few ways to see that history from the inside rather than from a passing car. Beyond the city, the coastline keeps changing character: Ilha Grande, once the site of a maximum-security prison that closed in 1994, is now known for beaches reachable only by boat and trails with no roads at all, while Arraial do Cabo’s water is often cited as among the clearest in the South Atlantic — cold, current-fed and startlingly turquoise, a genuinely different Brazil within a single long day from the city.