Spot reduction
The claim, as heard: "Do crunches for the belly, inner-thigh machines for the thighs — work the area and the fat there goes."
What the data show. Fat is stored in cells throughout the body and mobilised into the blood as a whole-body response to a deficit, then used wherever it is needed; a working muscle takes fuel from that shared supply, not from the fat lying on top of it. The trial usually cited assigned six weeks of daily abdominal exercise to one group and nothing to a control group, and found no difference in abdominal fat between them — the exercisers gained endurance and lost no more belly than the controls. It is a small trial of twenty-four people, and a later small trial has argued the opposite, so the honest reading is "the prevailing data say no" rather than "proven impossible". Where the fat goes from first is largely set by sex and genetics — which is why the belly is often last to go and the face first — and no exercise selection changes the order.
Verdict: false, on the prevailing evidence. Evidence grade C: one small randomised trial plus physiology, with a small dissenting trial acknowledged.
The grain of truth. Training the abdominal muscles makes them stronger and, once the fat over them thins, visible. Training the whole body raises expenditure and preserves lean tissue during a deficit. The fat above the muscle leaves on the body's schedule, not the workout's.
One sentence to remember: you can choose which muscle to work; you cannot choose where the fat comes from.