All the talk of bitcoin in recent years has overshadowed the real e-finance revolution: In Africa, India and now Eastern Europe, a service called M-Pesa has replaced banking for millions of people who don't have or, in fact, even need a bank account.

Safaricom, Kenya's leading mobile operator, majority-owned by a subsidiary of France's Orange and operated by the U.K.'s Vodafone, introduced M-Pesa — mobile money in Swahili — in 2007. Soon the system had an agent in just about every village and every corner of Nairobi's vast Kibera slum. Locals came to the agents with their phones — just plain old Nokias, not fancy smartphones — signed up and received a new menu from the operator, allowing one to transfer money to another mobile number.

M-Pesa could be cashed at an agent's — by sending a text message and receiving money then and there — and, eventually, at automated-teller machines, without the need for a debit card. Sending money to family in a remote part of the country or paying at a market stall was suddenly as easy as texting. Nobody was sending wads of Kenyan shillings on buses, hoping they would make it to relatives in Mombasa or Kitale, or carrying much cash around. M-Pesa was cheaper then a bank, and it was everywhere, with hand-painted signs for agents popping into view in the unlikeliest places.