TALLINN, Estonia ? Uber used to dominate ride-hailing in Poland and Kenya. Over the past two years, that started to change.

In Poland, a small competitor opened a rival service and began winning customers with cheaper fares and attracting drivers by charging lower commissions. In Kenya, that same upstart grabbed business by offering motorbike rides and letting passengers pay using a popular mobile payments provider.

In both countries, Uber responded by spending more money on new incentives to entice customers and drivers.

The rival that put Uber on the defensive is called Bolt. Based in Estonia, it was founded six years ago by a 19-year-old college dropout, Markus Villig. Since then, the company has turned into an unexpected success story by becoming Uber?s most formidable challenger in Europe and Africa.

?Transportation is a completely different space,? Villig said at Bolt?s offices inside a former furniture warehouse in Estonia?s capital. ?You will have these regional champions.? He added that Uber did not make Eastern Europe and Africa a priority because ?they have bigger battles elsewhere.?

Bolt is an example of a troublesome trend for Uber, the world?s largest ride-hailing company, which is set to go public next month at a valuation of as much as $100 billion. Everywhere the San Francisco company turns, a conveyor belt of new antagonists keeps emerging around the globe. In India, Uber is battling a service called Ola. In Brazil, it is dueling Didi Chuxing, a Chinese company that bought the local ride-hailing operator 99 last year. (Uber owns a stake in Didi.) And newfangled transportation companies, such as electric scooter providers, have popped up.

The multifront battle means that Uber, which is already spending billions of dollars to...