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One month into Russia's invasion of Ukraine, fire rained down on a shopping mall and high-rise buildings in Kyiv, as the outnumbered Ukrainian military waged intense battles to defend the capital and other key cities from falling under Russian control.

A barrage of strikes on cities have wreaked destruction across Ukraine over the past four weeks, but Russian forces appeared stalled outside major cities in the face of fiercer-than-expected Ukrainian resistance. NATO estimated on Wednesday that 7,000 to 15,000 Russian soldiers have been killed since the war started Feb. 24.

On Wednesday, the U.S. made a formal determination that Russian troops have committed war crimes in Ukraine, as some of the millions who have fled continue to recount tales of horror. As one woman told The Associated Press: "People are being killed day and night."

Here are some key things to know about the conflict:

WHAT IS HAPPENING ON THE GROUND?

The capital of Kyiv is still under fire. A barrage of shelling rocked the city on Wednesday, with rockets slamming into a shopping mall and high-rise buildings in the districts of Sviatoshynskyi and Shevchenkivskyi.

Destruction was extensive and fires from the shelling injured four residents, city officials said.

From a public park in Kyiv, mayor Vitali Klitschko said Russian bombardment had so far killed 264 civilians in the capital, including four children. As he spoke to reporters, explosions and loud gunfire echoed across the city.

Wednesday's shelling claimed the life of another journalist. The independent Russian news outlet The Insider said Russian journalist Oksana Baulina was killed in a Kyiv neighborhood.

Russian forces were also bombing the ancient city of Chernihiv in northern Ukraine, the governor said Wednesday, destroying a bridge that had been critical for evacuations and aid deliveries.

WHAT IS HAPPENING IN MARIUPOL?

Mariupol, a strategic port city on the Sea of Azov, has become a vivid symbol of the war's savage destruction.

Some 100,000 of Mariupol's prewar population of 430,000 remain trapped in the city, Ukrainian President Volodymyr Zelenskyy said. They are subject to relentless Russian bombardment from the sea and skies, and struggling to survive without heat, food or clean water.

Zelenskyy accused the Russians of seizing a humanitarian convoy that was trying to get food and supplies to residents. Deputy Prime Minister Iryna Vereshchuk said 11 bus drivers and four rescue workers were being held captive.

Zelenskyy said what's happening in Mariupol is "inhumane."

WHAT HAS THE AP DIRECTLY WITNESSED OR CONFIRMED?

Firefighters sprayed water on a smoldering residential building that was demolished by Russian shelling in western Kyiv early Wednesday. As the sound of fighting rumbled in the distance, fire service spokesperson Svitlana Vologda told the AP that the fire was the largest since the war began, in terms of requests for firefighters to respond.

Kyiv was shaken by a constant barrage of shelling Wednesday and plumes of black smoke rose from the western outskirts of the city. At dusk, air raid sirens wailed over the capital as attacks continued.

In the seaside city of Odesa, fondly known as the Pearl of the Black Sea, street musicians played under cloudless skies as people fled.

Odesa has so far been spared the worst of Russia's onslaughts, but a major attack on Ukraine's biggest port city seems inevitable. Anxiety is growing. The streets are stacked with sandbags and barricades. Tearful families waved goodbye to loved ones at the train station.

"I can't understand what has happened," said Igor Topsi, a musician.

WHAT ARE UKRAINIAN REFUGEES SAYING?

Some of the more than 3.5 million people who have fled Ukraine have shared nightmarish stories of death, destruction and the painful separation from loved ones.

Natalia Savchenko, 37, arrived in Medyka, Poland, on Wednesday and said the situation in the eastern city of Kharkiv is "terrible." She said there is no electricity or water, and children are not being given medicine or food.

"People are being killed day and night. They are shooting with everything they have," she said.

At the train station in Przemysl, Poland, Kateryna Mytkevich said her family was trapped in Chernihiv for three weeks and hoped the war would pass them by — but then "bombs began to fall."

"Our children are dying. My son had to stay in Chernihiv, I could only take my daughter with me. It hurts a lot." said Mytkevich, 39.

Volodymr Fedorovych, 77, also fled Chernihiv, saying: "There was nothing, there wasn't even bread." He said bread was brought in every three days, and on one day, he walked away from the bread line to get some tea when a bomb fell without warning.

"Sixteen people died and 47 were taken by ambulance, some of them without arms and legs. Horrible. There were one hundred people in that queue," he said. Ukrainian officials have said that 10 people were killed in a bombing of a bread line last week.

HAS RUSSIA COMMITTED WAR CRIMES?

According to the United States, yes.

Secretary of State Antony Blinken said the U.S. made the formal determination after a "careful review" of public and intelligence sources.

Blinken said there have been numerous credible reports of indiscriminate attacks and attacks deliberately targeting civilians. He said Russian forces have destroyed apartment buildings, schools, hospitals, shopping centers, and ambulances "leaving thousands of innocent civilians killed or wounded."

Blinken said the U.S. would work with others to prosecute offenders. The International Criminal Court at The Hague is already investigating.

The announcement comes as U.S. President Joe Biden headed to Brussels, where he is expected to roll out new sanctions against Russia and coordinate more military assistance for Ukraine. Biden described the possibility that Russia could use chemical weapons in Ukraine as a "real threat" and said it's an issue that world leaders will discuss at the NATO summit.

WHAT IS RUSSIA'S MILITARY PLANNING?

A senior U.S. defense official said Wednesday that Russian ground forces appear to be setting up defensive positions about 15 to 20 kilometers (9 to 12 miles) outside Kyiv, as they continue to make little to no progress toward the city's center.

The official, who spoke on condition of anonymity to discuss military assessments, said it appears Russian forces are no longer trying to advance into Kyiv and are instead turning priorities to the Donbas region, in what could be an effort to prevent Ukrainian troops from moving west to defend other cities.

In an ominous sign that Moscow might consider using nuclear weapons, a senior Russian official said the country's nuclear arsenal would help deter the West from intervening in Ukraine.

Dmitry Rogozin, the head of the state aerospace corporation, Roscosmos, said in televised remarks that Russia "is capable of physically destroying any aggressor or any aggressor group within minutes at any distance," He said Moscow's nuclear stockpiles include tactical nuclear weapons, designed for use on battlefields, and far more powerful nuclear-tipped intercontinental ballistic missiles. Roscosmos oversees missile-building facilities.

Rogozin, known for his bluster, did not make clear what actions would be seen as interfering.

— Associated Press writer Lolita C. Baldor in Washington contributed to this report.

HOW MANY RUSSIAN AND UKRAINIAN TROOPS HAVE DIED?

An exact figure has been hard to pinpoint, as official numbers have not been regularly released by either country.

NATO estimated Wednesday that 7,000 to 15,000 Russian soldiers have been killed — the alliance's first public estimate on Russian casualties since the war began. The official spoke on condition of anonymity under ground rules set by NATO.

Back on March 2, Russia said nearly 500 soldiers had been killed and almost 1,600 wounded.

The most recent figure for Ukraine's military losses came from Zelenskyy on March 12, when he said that about 1,300 Ukrainian servicemen had been killed.

— Associated Press writer Robert Burns in Washington contributed to this report.

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Follow the AP's coverage of the war at https://apnews.com/hub/russia-ukraine