IN JUNE 2007 a banker, or anyone else with $499 to spare, could try a novel distraction from work: Apple’s first iPhone had just gone on sale. In October 2008, after Lehman’s fall, another technological innovation was more quietly unveiled. A paper published online under the name of Satoshi Nakamoto described and advocated a form of electronic cash which people could send to one another without going through discredited banks. It was called bitcoin.

As banks have adapted to the crisis and its aftermath with varying degrees of success, the rest of the world has not stood still. Smartphones and, less visibly, cloud computing have transformed people’s daily lives—and hence their use of money. Consumers expect to be able to use the powerful computers in their palms to pay for goods or move cash around as easily as they can tweet, stream videos or share photos with friends. Corporate customers are equally demanding. Yet banks’ information-technology systems are a curious mixture of the old and rickety and the sleek and modern. Malevolent hackers continually probe for weaknesses as banks are striving to stay ahead.