From what I’ve heard from my coworker do actually flew:

Step 1: Attempt radio contact on local frequencies and guard.

Step 2: Try to lead you out of restricted air space

Step 3: Try to REALLY get your attention like doing precision fly so that you are unmistakably aware of them (like a really really close fly by). If this works, try step 2 again

Step 4: Really depends on where you are and/or who you are. If you are willfully violating air space and a civilian, you’ll probably get your certificate revoked and/or face. If you get near something really sensitive and probably are doing so purposefully despite attempts to get your attention, and you’re not over a densely populated area, you could get shot down.

Movies would have people believe that the jets are there to shoot down the errant jet. During the Cold War, this was entirely plausible and did happen. But more commonly, when a fighter jet is sent to intercept an unknown aircraft – perhaps one that has entered restricted or prohibited airspace – it may be just to have eyes on the situation.

Airspace is huge. The vastness of the air is like the vastness of the sea. Sometimes it’s an advantage because there’s fewer things to hit. But on the flip side, if an aircraft needs assistance, there might not be anyone for many miles in any direction. As for what an assisting fighter jet can do, the first is to establish navigational accuracy. History has shown that airplanes can get lost, and sometimes unfortunately end up hitting mountains or running into known obstacles or weather. A second aircraft can confirm the first aircraft’s position, since two separate aircraft having navigational problems is exceptionally rare.

The next thing is having eyes on the outside of the aircraft. Things like a damaged engine on a jetliner aren’t visible to the pilots, but there’s a chance the passengers or cabin crew can look. But damage to a rudder is impossible to see from inside the aircraft; I’m not yet aware of a commercial aircraft equipped with a tail-viewing camera. Checking the condition of the landing gear is also valuable information, if a jetliner has taken damage but still aloft.

Finally, if it should come to it, an assisting aircraft can be the pilot’s eyes, if for some reason the pilots can no longer see out their windscreen. At this point, the flight may already be close to the end but it may help avoid additional casualties on the ground. I’m reminded of the flight where volcanic ash sandblasted the windshield, or when a cargo jet had a fire onboard which filled the cockpit with thick smoke.

To be clear, neither incident was aided by fighter jets, but having an external set of eyes to give directions would have made things a little bit easier for the pilots. Other aircraft besides fighter jets can provide assistance, such as any helicopters or private pilots in the area. But of course, fighter jets are on-standby and can get to a scene very fast.

I can only speak for the UK and from a amateur perspective but here’s the rough breakdown:

90% of the time it’s likely a private pilot that’s wandered into a restricted airspace without realising it. Or a faulty radio or navigation equipment or a medical emergency. They’re politely escorted out.

9.9999% of the time is an adversarial nation testing the response time of the quick-reaction force defenses. They’re politely but forcefully escorted out. Maybe some insults traded over the radio but that’d be about as heated as it gets.

0.0001% they pose a threat and refuse to be escorted out. At that point it’s basically the same thing of asking “what would happen if someone climbed the fence to the White House and towards it and when the secret service pointed guns at them didn’t stop, would they get shot?”

It’s the pilot’s call at that point, but if they posed a threat to life then yes they probably would shoot them down.

Edit: there’s probably a ridiculous amount of zeros I’d need to add to the last point to indicate how unlikely it is but I can’t be arsed to add that many. Basically you might as well round down to 0%

Shoot it down, or just get it’s attention. A lot of the time there’s a radio fuckup. If some guy cruising in his Cessna sees a fighter pull up along side, he’s definitely switching to 121.5.

There was a commercial jet that was non responsive and the fighter could see the pilots passed out.

Otherwise be there to shoot it down quicker if it looks like it might be taking an aggressive action.