Ukrainian forces have broken through Russian lines on two fronts during audacious counteroffensives in territories Vladimir Putin recently declared to be part of Russia.

The big picture: Ukraine is recapturing territory with remarkable speed, but may have a narrowing window to gain ground before winter weather makes offensive operations difficult, and before Russia is able to flood in newly drafted soldiers to reinforce their lines.

Driving the news: Reports have been streaming in over the last several days of Ukrainian breakthroughs near Russian-held Kherson in southern Ukraine.

• Ukraine recaptured at least at least 10 villages in the Kherson region between Sunday and Tuesday, per Foreign Policy. Kherson is the only regional capital to fall since the invasion began, and recapturing it is a top Ukrainian objective.
• The recent gains came after a month of difficult fighting in the Kherson campaign had yielded only gradual progress. Ukraine seems to have steadily weakened the Russian lines before breaking through and forcing a retreat to the south, says Michael Kofman, an expert on Russia's military at CNA.
• If Russian forces continue to fall back, Ukrainian artillery will come within range of the Dnipro River crossings Russia uses to supply its forces in Kherson — potentially leaving the Russians penned in, and making even retreat difficult. "The Russian military position is not just precarious, but visibly deteriorating," Kofman says.

Meanwhile in the northeast, the key logistics hub of Lyman in northern Donetsk region fell to Ukraine on Friday.

• While the Kherson offensive had been telegraphed for months, the northeastern push seems to have caught the Russians by surprise. Ukrainian forces have captured an estimated 2,000 sq. miles there in less than a month.

What they're saying: Putin tacitly acknowledged the recent setbacks in on Wednesday but said, “We are working on the assumption that the situation in the new territories will stabilize.”

• State TV pundits have sounded unusually pessimistic in recent days, though they regularly repeat that Russia is at war with NATO — which is providing Kyiv with arms and intelligence — not just Ukraine.
• Putin's two big recent announcements — claiming that 15% of Ukraine is now Russia, and ordering the mobilization of an estimated 300,000 men — come with Russia in retreat on two fronts.
• Hundreds of thousands of Russians have fled to neighboring countries since the Sep. 21 mobilization order, but tens of thousands of draftees are also now preparing to deploy to Ukraine.

The other side: Ukrainian government accounts have been sharing videos of captured towns, soldiers and tanks, all underscoring the recent successes.

• There have been no similar successes on the Russian side for several weeks. However, analysts believe Ukraine's casualties in the Kherson offensive have been significant.
• The Biden administration announced a new $625 million security assistance package on Tuesday that includes four additional High Mobility Artillery Rocket Systems (HIMARS).

What to watch: It remains to be seen whether and when Russia's new recruits will be change the trajectory of the war, or at least prolong it. Kyiv and Washington must also contend with the possibility that if his choice is escalation or defeat, Putin could go nuclear.

Go deeper: U.S. grapples with risk of nuclear war over Ukraine