Turkey says it has shot down a Russian warplane that violated its airspace. Russian jets, in the area to bomb neighboring Syria, have violated Turkish airspace previously. Tensions between Russia and Turkey have been rising in recent weeks.

Russian President Vladimir Putin acknowledged the shoot-down but says the plane was in Syria, 4 kilometers from Turkey's border. He described Turkey as "backstabbing" Russia and accused it of financing ISIS.

Several videos have emerged that appear to show the body of the Russian pilot recovered from the plane.

Turkey is a member of NATO, making it a military ally of the US and most of Europe. NATO has called an emergency meeting over the incident. The risk of a major escalation between Russia and NATO is very low, but this may nonetheless have serious repercussions.

Why Russia might send a warplane into Turkey's airspace

It is certainly possible that if this Russian plane did cross into Turkish airspace, it was an accident; Russia has been bombing some targets along the Syria-Turkey border, after all. But Russian jets have committed enough such violations that it's also very possible this was deliberate.

Russian jets first crossed into Turkey's airspace in early October, just a few days after Russia began bombing targets in Syria. Both the US and NATO publicly warned Russia that this was extremely dangerous: Turkey is a member of NATO, meaning that the US and European powers are at least theoretically obligated to defend it from attack.

Russia and Turkey are on opposite sides of Syria's increasingly heated proxy war. Something like this may have been inevitable.

But there was every reason to expect that Russia's airspace violations would continue, in part because Russia had been doing the same for months against another set of NATO allies: the Baltic states of Estonia, Latvia, and Lithuania in northeastern Europe. Those Russian flights began shortly after Russia covertly invaded eastern Ukraine, which prompted Western sanctions against Russia.

When you ask Russia experts why Moscow would send its warplanes buzzing NATO airspace in Europe, they'll often point out that Russia's military is much weaker than America's and NATO's — and Moscow knows it. And indeed this military imbalance is something you hear Russian defense officials bring up constantly; this fact of their relative weakness is world-shaping for them.

So one way Russia has dealt with its relative weakness is by being more provocative, by demonstrating its willingness to raise the stakes and toe ever closer up to the line of outright conflict. The intended message of such flights isn't that Russia will deliberately start a war with the West — it won't — but rather that it is more willing to take on risk, so if the West doesn't want the headache it should just back down.

Russia's Syria intervention was already unpopular at home. It could become more so now.

In terms of Syria, then, those flights may be about Russia finding a way to assert its military presence, and preempt any Western effort to chase it off, by taking pushy and provocative steps like buzzing Turkish airspace.

That this was risky and dangerous may have been precisely the point: With its flights across NATO airspace in the Baltics, Russia was likely seeking to raise the stakes and hope that Western countries, wanting to avoid an incident like today's shoot-down, would take on the burden of deescalating. But that is not how things worked out with Turkey.

Why Turkey would shoot down the plane — and why this might surprise Russia

When Russian planes crossed into NATO airspace in the Baltics, as they did in several incidents last year and this year, NATO jets responded by scrambling to intercept the flights — and in one incident even came within mere yards of a collision — but never fired on them.

Russian officials can tend to see all of NATO as a unified block, and they may have concluded from these Baltic flights that Turkey wouldn't fire on them, either.

That Russia's flights are provocative and dangerous may be precisely the point

Turkey is different. Its foreign policy is, depending on your perspective, either unusually assertive or unusually reckless (or both). This is especially true in Syria, where it has long been involved in aiding the flow of rebels who are fighting Syrian leader Bashar al-Assad.

Turkey is also at war with Kurdish groups at home, and has bombed Kurdish rebels in Iraq. It has bombed ISIS some, but only sparingly; while it does not support the group, it is not particularly focused on fighting it.

All of this is to say that while Moscow may believe NATO controls Turkish military actions, in fact there has been significant disagreement between Turkey and its NATO allies over Middle Eastern military action, and Turkey has been more aggressive than its allies would like.

Russia has been bombing ethnic Turkmen in Syria, enraging Turkey

There's also another factor here. Russia has, in just the past week, been bombing Syrian rebels who are part of the Turkmen ethnic group. This enraged Turkey, which summoned the Russian ambassador to demand Russia stop its bombing. Turkey considers ethnic Turkmen to be something like unofficial Turkish citizens.

Turkish Prime Minister Ahmet Davutoglu called the Russian-bombed Syrians "our Turkmen siblings" and said "we are condemning this barbarian attack in the strongest way." A statement by Turkey's foreign ministry warned the bombing "may lead to serious consequences."

That is not to say that Turkey necessarily shot down the Russian plane in cold-blooded vengeance for Russia bombing ethnic Turkmens. But the bombings may have contributed to already-rising tensions between Turkey and Russia over Syria. And it's not just the flights: Russia intervened in Syria to support Bashar al-Assad, but Turkey has been involved in Syria for a few years seeking to topple Assad. They're on opposite sides of a deadly serious proxy war. Escalation was not out of the question.

What happens now? Not war, but this could still be significant.

If you're worried about this spiraling into World War III, take a breath: There is every reason to believe that both Russia and NATO will seek to deescalate. Neither cares enough about enforcing Syria-Turkey border zone air rights to escalate much over this.

Still, Russia and NATO are both taking this very seriously. Putin has already issued a public statement accusing Turkey of "backstabbing" Russia — and also saying publicly that Turkey finances and supports ISIS (this is not, as best we know, true). NATO is planning on holding an "extraordinary" meeting to discuss the incident at 4 pm GMT (11 am EST) on Tuesday.

Relations between Turkey and Russia have previously been quite good, though they've been souring since Russia got involved in Syria. They may deteriorate further now. That's significant for both countries, especially economically. Turkey imports most of its energy from Russia — 60 percent of its natural gas imports are Russian — and Turkey had a $20 billion deal with a Russian state-owned firm to build a nuclear power plant.

This doesn't mean that Russia is going to turn off the tap or that Turkey is going to cancel all its natural gas imports, but if there's going to be retaliatory escalation between them, it may well be in this economic sphere.

The similarities between Putin and Turkish President Recep Tayyip Erdogan may be among the most important factors here. Both are nationalists who rely on military power and who are seeking to cast ever-more-assertive involvement abroad — having two such escalation-prone leaders going head to head is dangerous.

Both leaders are also deeply concerned with looking good at home, which means that neither wants to look like he's backing down. At the same time, both are canny and pragmatic. They'll both want to look tough here — and that makes them both more likely to escalate — but neither is crazy enough to let this spiral out of control.

Mark Galeotti, a Russia expert who teaches at NYU, explained well why everyone involved is probably going to try to deescalate here:

I suspect neither Moscow nor, at the very least, the other European NATO powers will want to let this go too far. Russia cannot fight hot diplomatic wars on too many fronts, and Europe clearly wants Moscow to be part of the solution in Syria and maybe Ukraine, too. And, frankly, there is in many capitals concern about Turkey, its agenda and its role in the region.

Still, "I don’t imagine that will be the end to it," Galeotti says. "I would expect some uptick in ‘mischief’ – perhaps some support for the Kurds or other violent extreme movements, for example – as well as a more assiduous campaign to push back and stymie Turkish regional ambitions."

Russia was already showing hints that it considered its Syria intervention a mistake

One important question is whether this will have any ramifications for the international peace talks to end Syria's war. Russia has been making ever-so-tentative signals that it might be willing to make some real concessions to end the war, maybe even help to nudge out Assad.

This incident, then, could lead Russia to conclude that its Syria involvement is getting too costly.

While Russian leaders don't really, as a rule, admit mistakes — that's not how they teach it in the Moscow school of diplomacy, as I heard one senior US official put it — there are indications that it was beginning to see its Syria intervention as a mistake.

A number of Russians have reportedly died in the fighting, and they don't have much to show for it. In October, Russian and Iranian forces helped Assad's army launch a big military campaign to retake territory from the rebels — and it largely failed.

Russia's Syria intervention is unpopular at home, and Putin is extremely sensitive to public opinion. A September poll by Moscow's Levada Center found that only 39 percent of respondents said they supported Russia's policy toward the Assad regime. When asked what Russia should do for Assad, 69 percent opposed direct military intervention. A tiny 14 percent of respondents said that Russia should send troops or other direct military support to Syria.

That's a pretty sharp contrast to Russia's policy toward Ukraine, which has been enormously popular with Russians. Putin's first, second, and third concerns have always been to maintain his own rule at home. With the economy in shambles, public opinion is crucial for that. Now that footage is emerging of a dead Russian pilot, Russian public opinion could become even more skeptical of the Syria intervention. And Putin will likely respond to that.

At the same time, this could lead Putin to harden his position on Syria — to seek to raise the stakes and make this about avenging Russian honor as a means to shore up public support for the war. That's probably not the most likely outcome, but it is a possibility.

VIDEO: The war in Syria, explained