It has been little more than a decade since the Iron Curtain came tumbling down, and retail banking in Eastern Europe’s most advanced markets has developed at a startling pace. Drab state-run branch offices, with their long lines of people waiting to deposit or withdraw cash, have largely disappeared. In just a few years, the region’s best banks have matched the service revolution—retail brokerage, mutual funds, ATMs, call centers, and Internet and mobile banking—that took five decades to mature in the West. Now, as these former Soviet bloc countries line up to join the European Union and embrace its more predictable economic regime, Western-owned banks are competing with streamlined incumbents in retail-banking markets that have far higher revenue and profit growth than do those in Western Europe or the United States.

Yet Eastern European markets are maturing. Overall investment has fallen from its peak, and while some foreign-owned banks continue to expand, others are leaving as intensified competition and convergence toward Western European market conditions begin to separate the winners from the also-rans. Western bankers will be familiar with the challenges—notably an ever-tougher battle for the all-important affluent-customer segment and a growing need to counter pressure on margins by...