The success of Ukraine’s secret incursion into Russia is clear. Ukrainian forces pushed past two lines of Russian defenses in the southwestern region of Kursk and moved through Russian highways and villages with little resistance. Since the operation began 11 days ago, they have gone beyond Kursk to the neighboring region of Belgorod, putting other communities on edge and rattling Moscow.

The ultimate strategy and goals of the invasion, though, are still murky. Western allies, including the United States and Germany, say they are watching and monitoring the situation but letting Ukraine lead the way. Even the Ukrainian leadership seems surprised by the extent of the operation’s initial success, the first time that Russia, a nuclear power, has been invaded since World War II.

So now what?

Ukraine has several options.

Ukrainian forces could try to keep pushing further into Russia. They could dig into the territory they now hold and try to defend it. Or, battered by continual losses in eastern Ukraine, especially this week near the strategically important city of Pokrovsk, they could decide that they have made the point to the West, and to Moscow, that Russia is not invincible. In that case, they could then pull back.

“We are playing here a bit on the psychological point that great powers do not lose their territories,” said Mykola Bielieskov, a senior analyst from Come Back Alive, a foundation that provides support to members of Ukraine’s military. If Russia loses, “it means that they are not that big.”

There are vulnerabilities for both sides.

Ukrainian officials have told senior United States civilian and military officials that the operation aims to create an operational dilemma for the Russians — to force Moscow to divert troops off the front lines in the eastern Ukraine region of Donetsk, where they have made slow but steady progress for weeks.