Over the past two decades people across the world have seen digital services transform the economy and their lives. Taxis, films, novels, noodles, doctors and dog-walkers can all be summoned with a tap of a screen. Giant firms in retailing, carmaking and the media have been humbled by new competitors. Yet one industry has withstood the tumult: banking. In rich countries it is perfectly normal to queue in branches, correspond with your bank by post and deposit cheques stamped with the logo of firms founded in the 19th century.

Yet, as our special report this week explains, technology is at last shaking up banking. In Asia payment apps are a way of life for over 1bn users. In the West mobile banking is reaching critical mass—49% of Americans bank on their phones—and tech giants are muscling in. Apple unveiled a credit card with Goldman Sachs on March 25th. Facebook is proposing a payments service to let users buy tickets and settle bills (see article).

The implications are profound because banks are not ordinary firms. It is one thing for Blockbuster Video to be wiped out by a technological shift, but quite another if the victim is Bank of America. It is not just that banks have over $100trn of assets globally. Using the difficult trick of “maturity transformation” (turning deposits that you can demand back at any time into long-term loans) they enable savers to defer consumption and investment and borrowers to bring them forward. Banks are so vital that the economy reels when they stumble, as the crisis of 2008-09 showed.

Bankers and politicians may thus be tempted to resist technological change. But that would be wrong because its benefits—a leaner, more user-friendly and more open financial system—easily outweigh the risks.

Banking is late to the smartphone age because entrepreneurs have been put off by regulations. And, since the financial crisis, Western banks have been preoccupied with repairing their balance-sheets and old-fashioned cost-cutting. Late is better than never, however. Several new business models are emerging. In Asia payment apps are bundled with e-commerce, chat and ride-hailing services offered by firms such as Alibaba and Tencent in China and Grab in South-East Asia. These networks link to banks but are vying to control the customer relationship. In America and Europe big banks are still more or less in control and are rushing to offer digital products—JPMorgan Chase can open a deposit account in five minutes. But threats loom. Mobile-only “neobanks” that do not bear the cost of branches are nibbling at customer bases. Payments firms like PayPal work with Western banks but are expected to capture a greater share of profits. Lucrative niches like foreign exchange and asset management are being harried by new entrants.

The pace of change will accelerate. Younger people no longer stay with the same bank as their parents—15% of British 18- to 23-year-olds use a neobank. Tech firms that people trust, such as Apple and Amazon, are natural candidates to grow big financial arms. The biggest four American banks are spending a total of over $25bn a year on perfecting better customer applications and learning to mine data more cleverly. Venture-capital firms invested $37bn in upstart financial firms last year.

The benefits of technological change are likely to be vast. Costs should tumble as branches are shut, creaking mainframe systems retired and bureaucracy culled. If the world’s listed banks chopped expenses by a third, the saving would be worth $80 a year for every person on Earth. In 2000 the Netherlands had more bank branches per head than America; it now has just a third as many. Rotten service will improve—it is easier to get money to a friend using a chat app than it is to ask your bank to transfer cash. The system will get better at its vital job of allocating capital. Richer data will allow banks to take risks that currently baffle underwriters. Fraud should be easier to spot. Lower costs and the democratising effect of social media will give more people better access to finance. And more firms with good ideas should be able to get loans faster, boosting growth.

Yet change also poses risks. Because the financial system is embedded in the economy, innovation tends to create turbulence. The credit card’s arrival in 1950 revolutionised shopping but also sparked America’s consumer-debt culture. Securitisation lubricated capital markets in the 1980s but fuelled the subprime crisis. In addition, it is unclear who will win today’s battle. One dystopian scenario is that power becomes more concentrated, as a few big banks learn to exploit data as ruthlessly as social-media firms do. Imagine a crossbreed of Facebook and Wells Fargo that predicts and manipulates how customers behave and is able to use proprietary economic data to squeeze rivals.

Another dystopia involves fragmentation and destabilisation. Banks could lose depositors to untested neobanks, creating a mismatch between their assets and liabilities that could lead to a credit crunch. If bank customers transact via tech or payment platforms, banks could end up with huge balance-sheets but without a direct connection to their clients. If they thus became unprofitable, they could be broken up, with the job of financing mortgages and absorbing short-term savings left entirely to capital markets, which are volatile.

To tap the benefits of technology safely, governments should give consumers control over their data, protecting privacy and preventing firms hoarding information. Innovation-friendly regulation would help; in 2017 the industry faced a regulatory alert every nine minutes (see article). And governments should keep the system’s safety buffers at today’s overall size (global banks hold $7trn of core capital). If new entrants are properly capitalised, central banks could extend to them the lender-of-last-resort facilities that provide shelter in a storm.

Banking’s dirty secret is that it is backward, inefficient and hidebound. Banks have formidable lobbying power, however. Wary of change, customers, politicians and unions complain when branches are closed and jobs cut—witness the recent collapse of a German mega-merger that depended on both. Regulators love dealing with a few big firms. The thing is that global growth is sluggish and productivity gains are hard to come by. A smartphone revolution in finance offers one of the best ways to boost the economy and spread the benefits.