They do whilst you're wearing it - although the flab needs to go somewhere, so it goes under the trainer or above it, it doesn't disappear. It also squishes your organs, though, and ruins your posture. Your waist won't actually "train" to look slimmer.
It doesn't even really work as an incentive to eat less because you see the bulge and think a magnum won't hurt that much.
Biologically I knew this would be the case but I tried it anyway. My doctor laughed. And then made me promise to stop wearing it.