Air traffic controllers can use both primary and secondary radar to keep an eye on planes while they’re nearby (usually within a few hundred miles or so), but there are limits to what they can detect. Aviation reporter Steven Trimble told NPR:
The fact is an aircraft can fly off radar. Once it gets over the water, radar coverage is not nearly as robust as it is on land. And, of course, if you go below certain altitude, because of the curvature of the Earth, radar can't see you. And that appears to have happened here.
But Wired points out that it’s possible that a private or military aircraft with more flexible radar capabilities might have picked up clues about Flight 370 without realizing it. A former Marine Corps pilot and current aviation consultant, Col. J. Joseph, told Wired, “I would be very surprised if, on somebody’s radar data, this event was not recorded.”
David Esser, a professor at Embry-Riddle Aeronautical University, agrees that it’s possible. “Someone could have picked up a ping from them before they disappeared,” he says. But Esser warns that even these clues might not lead anywhere. “Let’s say the plane broke up at 40,000 feet. This stuff is going to be spread over a pretty wide area. It’s a big ocean.”