The Jaeger-LeCoultre Reverso is the rectangular watch that turns over in a metal frame. One face is the dial you read. The other face is a solid back or a second dial, depending on the version. The trick is the frame, not a round bezel.
How it differs
It does not wear like an Oyster. The case slides and flips. The lugs, when it has them, are part of the carrier, and a strap or a bracelet has to follow that rectangle. End links on a bracelet version are short and specific. A round-watch end link will not do. The crystal is flat or slightly raised, and there may be a second crystal on the reverse. Count them before you describe a scratch.
The movement is small relative to the frame. A seconds hand, if the version has one, should move smoothly. A quartz version steps. Say which motion you see instead of guessing the caliber from the case shape.
Common mods
Strap changes are common. Bracelet changes are rarer and fussier, because the end links have to meet the carrier. Crystal replacement is the other usual job, often after a line across the front glass. The new crystal should sit in the same plane as the old one, and the frame should still slide. Hands are occasionally refinished. After that work, they should clear the chapter ring and should not touch the glass when the case is turned over in your hand.
What to check on a used piece
On a used Jaeger-LeCoultre Reverso, check the bracelet end links where they meet the case, the crystal over the dial, and the movement. Flip the case ten times. It should lock at each end. A case that flops is a frame problem. Write that down, and do not treat it as a dial problem.
The notes for those parts are the bracelet, the case, and the movement.