Some architectural styles boast examples from many great architects. But there are some architects that defy categorisation to do something gloriously strange – and here's where to find them.
Where? Barcelona, Spain
If you can't think of any other exponents of Catalan modernism, that's largely because it's just Gaudí. His weird and wonderful efforts incorporated stained glass, ceramics, ironwork and carpentry. Now seven of his works are World Heritage-listed, and although the Sagrada Familia cathedral is his best known, Park Güell hosts the greatest unified collection of buildings. See parkguell.barcelona
Where? Vienna, Austria
Before moving to New Zealand, Hundertwasser let his fantastical, straight-line averse and unruly whims loose on several Vienna buildings. Most famous is the Hundertwasser House apartment block, which has undulating floors, trees growing in rooms, garish colours and all manner of weird bulges. He also applied similar tactics to the Spittelau incinerator, north of the city centre. See kunsthauswien.com
Where? Bilbao, Spain
Gehry's asymmetric marvels can be found all over the globe – notable examples include the Dancing Building in Prague, the Walt Disney Concert Hall in LA, the Pritzker Pavilion in Chicago and the UTS business school in Sydney. But the one that proved a single bizarre building could change a city's fortunes was the Guggenheim in Bilbao, a swirling vision in titanium that looks from certain angles like the unravelling ribbon on a gift-wrapped present. See Guggenheim-bilbao.eus
Where? Riga, Latvia
Several architects had their own take on art nouveau, but none were quite as full on as Eisenstein. He threw everything at his buildings – including fake floors, open-mouthed figureheads, Egyptian motifs and toadstool-shaped windows. Most of them can be found in Riga's Art Nouveau Quarter along Alberta iela and Elizabetes iela. See livariga.com
Where? Innsbruck, Austria
The Iraq-born curve enthusiast has left her handiwork all over the world – straight line-phobic examples include the Riverside Museum in Glasgow, London's Olympic Aquatic Centre and the Dongdaemun Design Plaza in Seoul. But she arguably had her biggest impact in Innsbruck, where the Nordekette cable railway stations look like they have icebergs on top and the Bergisel ski jump looks like a giant virtual reality helmet. See Innsbruck.info
Schereen is part of the team behind the CCTV Headquarters in Beijing, which has an optical illusion look not dissimilar to an Escher staircase. But he's sprinkled his magic further in Singapore with the Interlace, which looks like Jenga bricks hurriedly piled together on top of each other, and DUO, which has the vibe of a Transformer midway through changing into a giant death robot. See visitsingapore.com
Where? Rotterdam, Netherlands
Piet Blom is notorious for his Cube Houses, which might not seem especially weird – after all, most houses are more or less cubic – until you see the way they're positioned. This series of structures in Rotterdam has the building 'balancing' on the corner of the cube, with everything else made to fit the angle in a laughably inconvenient manner. One of them's open to visitors. See Rotterdam.info.
Where? Montreal, Canada
Safdie's best known work is the audacious Marina Bay Sands in Singapore, where a surfboard-esque roof stretches high across the top of three towers. But while his other designs are striking, none stand out quite as much as his debut project, Habitat 67 in Montreal. This housing complex is comprised of 354 identical concrete blocks, arranged in seemingly higgledy-piggledy fashion, jutting out at all angles over 12 storeys. See habitat67.com
Richard Buckminster Fuller
Where? Dearborn, Michigan.
Buckminster Fuller became obsessed with the idea that cheap 'Domehomes', created using lattice-like structures that evenly distribute weight, could solve housing crises. He lived in one himself – it's in Carbondale, Illinois – although his most famous 'geodesic dome' is the ball-like Biosphere in Montreal. He also tried to push circular, pre-fabricated homes called Dymaxion Houses, which had waterless toilets shrink-wrapping waste. One's on display at the Henry Ford Museum in Michigan. See thehenryford.org
Where? Sydney, Australia
We take the Sydney Opera House for granted now, but don't forget how radically different it was when it was first unveiled. Utzon was only the second architect to have his building recognised as a World Heritage site within his lifetime. The Dane gave Australia an international icon, but he also did plenty in his homeland – including the L-shaped Kingo Houses in Helsingør, which combined traditional Danish farmhouse style with Islamic-influenced central courtyards. See sydneyoperahouse.com