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: