The Ukrainian vessels were attempting to pass through the Kerch Strait, a narrow artery linking the Black Sea and the Sea of Azov. Russia has effectively controlled the strait ever since it annexed Crimea in 2014.
In response, Ukrainian President Petro Poroshenko declared 30 days of martial law in border areas over what he called a violation of international law. Russia blamed the incident on Ukrainian provocation.
U.S. Ambassador to the United Nations Nikki Haley and Secretary of State Mike Pompeo joined other Western leaders in pointing the finger squarely at the Kremlin and alleged Russia aggression. Their boss — often accused of being soft on President Vladimir Putin — appeared reluctant to apportion blame.
"We don't like what's happening either way," President Donald Trump told reporters Monday.
The sailors were taken to the Crimean port of Kerch, where local media released a video purporting to show some of the men speaking on camera. They explain they entered Russian territorial waters and received warnings from Russian border control vessels to leave the area.
One of the men said he was aware their actions were "of a provocative nature."
The Ukrainian military confirmed on Facebook that the men in the video were its sailors.
However, such videos must be treated with extreme caution because it's not clear what was said before or after these edited extracts, nor whether the sailors were under duress.
The men appear relaxed, but the head of Ukraine's security service, Vasyl Hrytsak warned that they were under "psychological and physical pressure" while in detention.
Both countries disagree on the detainees' legal status.
Ukrainian Foreign Minister Pavlo Klimkin called them "prisoners of war." This means they would be protected by the Geneva Convention, which states POWs should be treated humanely, shielded from "public curiosity" and immune from prosecution for taking part in hostilities.
The International Committee of the Red Cross in Ukraine told NBC News it had asked for access to the detainees.
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"What's most important now is that those wounded and detained in relation to this situation are treated humanely, that the wounded get an adequate medical care and that the detained crews' members can communicate with their loved ones," ICRC spokeswoman Jana Bauerova said.
Russia, on the other hand, denies the men are POWs. It calls them trespassers who will be "prosecuted in strict accordance with the law," the state-run TASS news agency quoted Putin's spokesman Dmitry Peskov as saying.
A local court will determine the fate of the sailors but Ukraine's foreign minister suggested the decision would ultimately be in the hands of the Russian president.
"In reality, we clearly understand that the decision can only be made on Putin's level," Klimkin told Ukrainian television. "That’s where our efforts are at."
Cutting through the claims and counterclaims, the dispute largely boils down to one thing: Crimea.
When Russia and Ukraine were relatively friendly, they shared the Sea of Azov and the Kerch Strait as part of a 2003 agreement.
That was all fine until 2014, when Russia annexed Crimea. This gave it control of not just one but both sides of the strait.
Although the 2003 agreement still stands in theory, Russia now demands that all vessels, including those from Ukraine, to request permission before they pass through.
In May, it opened the $3.69 billion Crimea Bridge, cementing its grip on this crucial bottleneck. Independent observers have pointed out that the bridge's span is lower than international standards, putting a permanent cap on the size of ship able to enter the Azov.
The move has caused huge delays in recent months, leading to claims Russia is trying to blockade Ukraine's ports and transform the Azov into a de facto Russian lake.
Some Western critics say this is all part of the Kremlin's tactic of "creeping annexation," a ploy to subtly recoup territory from its old Soviet allies.
Russia has been adamant its actions in the area are legally justified, and points out Ukraine has detained one of its own ships in this region.
It was against this backdrop that Russia claimed the three Ukrainian ships had entered its waters Sunday, ignoring verbal cautions and even warning shots.
Coordinates offered by officials and analysts on both sides suggest the vessels had been in Crimean waters, which Russia regards as its "territorial sea."
The problem with this is that most countries in the world, including the U.S. and almost all of Europe, say Russia's annexation of Crimea is an illegal occupation. They don't recognize these waters as Russian, and therefore say Moscow has no grounds to stop ships, let alone fire at them.
On this fundamental principle alone Russia's actions Sunday broke international law, according to Valentin Schatz, research associate in public international law at Germany's University of Hamburg.
He said that on a practical level, it could be argued Ukrainian ships have an obligation to notify Russian authorities and cooperate as they pass through the strait. Ukraine says it did this; Russia says that's not true.
In any case, Ukraine insists that its ships fled back out into international waters when they were shot at and seized.
Even if one were to accept that Crimea is now part of Russia, the Kremlin's legal case for firing at Ukrainian ships is shaky, Schatz added. Using force and detaining foreign warships "may only be used in exceptional circumstances," he said.
While international law is firmly on Ukraine's side, the local reality is different, according to Balázs Jarábik, a nonresident scholar at the Carnegie Endowment for International Peace.
"For Russia the security of the Kerch bridge is the utmost priority, and that requires Russia to minimize the Ukrainian military naval presence," he said.
Moscow is already embroiled in a conflict in eastern Ukraine, where Russian-backed separatists have been fighting a war against Kiev's troops, a four-year conflict that's claimed more than 10,000 lives.
Instead, the use of force against Ukraine is more likely an attempt to "expose the helplessness of the Ukrainian side" and tighten Russia's newfound grip on the Sea of Azov, four experts based at the Centre for Eastern Studies wrote Monday.
Western leaders have expressed "deep concern" at the events, but it's unclear whether this will translate into concrete action. Ukraine has called on the U.S. and Europe to levy more sanctions on Moscow.
Another option open to them is to provide Ukraine with assistance such as radars and anti-ship missiles, according to Michael Carpenter, a former deputy assistant secretary of defense at the Pentagon.
The U.S. currently has around 200 soldiers stationed as advisers in Ukraine but they are in the west of the country, hundreds of miles from Crimea and fighting in the east.
The crisis has had political implications too. On Monday, Poroshenko gained parliamentary approval to impose martial law in some of the country. Many experts had feared he would use this to postpone March's presidential election as he trails badly in the polls.