Sydney Opera House; Sydney, Australia

It's one of the world's most recognizable buildings, but the Sydney Opera House was an absolute headache to build. After selecting Danish architect John Utzon's unique design, the Australian government pushed for an early start to construction, fearing possible public backlash. Unfortunately, Utzon was still working on his final designs—something that led to significant problems later, including having to rebuild the structure's roof-supporting central podium columns.Bad weather and other unforeseen woes slowed construction almost immediately. Then, in 1966, a clash between Utzon and Australia's new government led to the architect's resignation. He vacated the country with his family and left behind an incomplete shell. A team of new architects eventually completed the opera house and it officially opened in 1973, albeit 10 years after its initial completion date and at a cost of $102 million—more than 14 times the original budget.Despite the difficulties, the Sydney Opera House exhibits several impressive engineering feats. It's one of the first structural designs worldwide to use Araldite, a synthetic resign adhesive for bonding metals, in its construction, and was one of the earliest uses of digital structural analysis.