After years of shunning North America and Europe in favor of exotic locales that promised oil in far greater quantities at a much lower cost, the industry’s largest players have come crawling back. The reason? Those big projects have been difficult to pull off and haven’t made up for declining production in more mature regions like the U.S. Last year the five largest U.S. and British oil companies—ExxonMobil, Royal Dutch Shell (RDSA), BP (BP), Chevron (CVX), and ConocoPhillips (COP), which together account for 11% of worldwide output—saw their oil production slide 3%, to 10 million barrels per day. Those shrinking supplies are one reason that oil now tops $125 a barrel.