March 2, 2022 5:39 PM EST

United Nations members voted overwhelmingly Wednesday afternoon to condemn Russia’s unprovoked invasion of Ukraine and to express “grave concern” about ongoing Russian attacks on civilian facilities, which have intensified in the past week. Russian forces have attacked a hospital in the Donetsk region of eastern Ukraine, an administrative building in Kharkiv, and a pre-school in northeastern Ukraine, according to Amnesty International and the United Nations.

“We stand together in holding Russia accountable for its violations of international law,” Linda Thomas-Greenfield, the U.S. ambassador to the U.N., said Wednesday. At least 536 civilians, including at least 13 children, have been killed since Feb. 24, according to the United Nations Human Rights Office of the High Commissioner, although researchers warn the real number is likely much higher.

The U.N. formal condemnation comes on the heels of a volley of calls for an investigation into whether Russia is committing war crimes in pursuing its “special military operation” in Ukraine. A group of 39 countries called on the International Criminal Court (ICC) to investigate Russia’s actions, and U.S. Sen. Lindsey Graham and Rep. Victoria Spartz, who was born in Ukraine, plan to introduce a resolution urging the ICC and a different international court, the International Court of Justice (ICJ) to launch investigation into whether Russian forces are committing “war crimes and crimes against humanity.” The ICC’s prosecutor’s office announced Monday that it “would proceed with opening an investigation” into the matter.

Whether Russia’s military actions in Ukraine technically qualify as “war crimes” under the international rules of war is now an open question. What can be done about it is another. International institutions, including the U.N., the ICJ, the ICC have ways that they can punish and isolate Vladimir Putin’s regime, but the extent to which they use those levers depends on the unity and support of powerful member states.

In the fog of battle and misinformation, one thing is clear: Russia has already violated international law by invading Ukraine, says John Bellinger, adjunct senior fellow for international and national security law at the Council on Foreign Relations (CFR), a nonpartisan think tank. The modern rules of war clearly prevent U.N. member states from using force against the “territorial integrity or political independence of any state.”

“What we don’t know yet, but the world will be watching closely, is whether, having invaded Ukraine, will Russian military forces be committing war crimes?” he adds. “Or have they already committed war crimes in Ukraine?”

What are the rules of war?

The rules of war, also known as international humanitarian law or the law of armed conflict, are drawn largely from international treaties including the Geneva Conventions, the UN Charter, and the Hague Conventions, along with generally accepted norms, experts say. These rules, which are broadly designed to limit unnecessary brutality in warfare, have existed in some form since the first Geneva Convention of 1864, which established that all wounded soldiers, regardless of nationality or affiliation, should receive medical care.

The rules have changed over the decades as technology has advanced. Amendments to the Geneva Convention adopted in 1949, for example, make clear that civilians should never be a target in war and that prisoners of war must be treated with adequate care.

The modern rules of war focus on the protection of “civilian objects,” an umbrella term that includes schools, hospitals, homes, and places of worship or places non-combatants are attempting to conduct their daily lives. Unless intelligence indicates that the “civilian object” is being used for military purposes, it is considered a war crime to target it, according to Human Rights Watch (HRW), an international human rights advocacy organization. Demonstrating intention, in other words, is key.

Read more: Russia Faces War Crime Accusations as Civilian Casualties Grow

If Russia is indeed found to be intentionally targeting civilian areas without a military purpose, that would amount to a war crime, Bellinger says. If instead it is killing civilians as collateral damage in its military operation, then it’s not clear that counts. On Wednesday, when a reporter asked President Joe Biden if Russia was deliberately targeting civilians, he responded, “they are.” (He responded to a follow up question asking if Russia’s actions constituted war crimes saying, “it’s too early to say.”)

Several humanitarian organizations including Amnesty International’s Crisis Evidence Lab and and HRW are documenting cases in which Russian attacks kill or injure Ukrainian civilians, in instances that may constitute war crimes. “We’re very, very concerned that Russia is, sadly, continuing on with its shameful track record on targeting, deliberately or not, innocent civilians who should never be targeted under the laws of war,” Marie Struthers, Amnesty International’s regional director of Eastern Europe and Central Asia, tells TIME.

The ICC, the international court system that allows individuals to bring charges against foreign governments, announced on Monday that it would launch an investigation into the matter. Established in 1998 after 60 countries—not including the U.S.—ratified a treaty known as the Rome Treaty, the ICC has jurisdiction to bring charges against individuals for acts of genocide, crimes against humanity, war crimes, and the “crime of aggression”—which includes “the use of armed force by a State against the sovereignty, integrity or independence of another State,” according the court’s description. Since the ICC became a functioning court in 2002, it has tried 30 cases.

The ICC’s Office of the Prosecutor is imbued with the power to investigate potential crimes, though both the investigations and the resulting prosecutions can take years. After Russia’s annexation of Crimea in 2014, Ukraine accepted the ICC’s jurisdiction over alleged crimes occurring on its territory. Cases against Russia resulting from that military incursion remain ongoing today.

On Saturday, Ukraine filed additional charges before the ICJ, the judicial body of the United Nations, alleging that Russia used false claims that Ukraine was committing genocide against Russians as pretext for its invasion, according to a public statement by the ICJ. There is no evidence that Russia’s allegations are true, Bellinger says. “Putin is using the language of international law—terms like ‘genocide’ and ‘self-defense,’ to throw up a smokescreen to cloak his actions in the language of international law,” he says.

Even if Russia is committing war crimes, can it be held accountable?

If Russia is found to have committed war crimes, what comes next isn’t clear, experts say. The ICC notes that, while it is actively investigating whether Russia committed war crimes in Ukraine, Russia is not party to the treaty that formulated the court. Which is to say that Russians on trial could argue that the court has no legal authority over them. “If there is an indictment against any Russian officials, it is very unlikely that they would ever be arrested and taken to the Hague,” Bellinger says.

Read more: Ukraine’s Secret Weapon Against Russia: Turkish Drones

Marie Struthers of Amnesty International says international institutions have not always had as much sway as some would like. “On Russia, traditionally these international mechanisms have been rather weak,” she says. But there may be reason to believe that this time will be different. The scale of Russia’s invasion this time around has been far more intense than in 2014, and so has the international response. “Both of which lead me to say, not with 100% certainty, but that maybe we will come out of this particular horrible conflict with some mechanism that’s more robust in terms of holding the Russian military and perhaps even the President accountable,” she says.

Bellinger is also hopeful that the scale of Russia’s attack will force the international bodies to act. “Russia’s invasion of Ukraine poses perhaps the most serious challenge to the UN Charter in 75 years, and it will put both international law and international institutions under pressure,” he says. “We’ll have to see whether international institutions like the UN, the International Court of Justice, the International Criminal Court, and the General Assembly can rise to this challenge.”

Read more: Here’s What You Can Do to Help People in Ukraine Right Now

The U.N. vote Wednesday to condemn Russia’s war in Ukraine was an almost entirely symbolic gesture, but in coming days and weeks, the General Assembly could take more forceful steps, including urging that Russia be ejected from certain U.N. bodies and committees, calling for further investigations, or encouraging further sanctions against Russia, providing leeway for countries that have so far hesitated to join the sanctions. The UN Human Rights Council is now considering whether to open an investigation into human rights violations in Ukraine.

“The General Assembly is somewhat limited on the actions that it can take,” Bellinger says. “But it can still isolate Russia, and urge all the rest of the countries in the world and international organizations to take actions to further condemn and isolate Russia. It’s not quite the same as a law, like our Senate passing a law, but it still can be very consequential.”

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Write to Jasmine Aguilera at jasmine.aguilera@time.com.

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