Why does my CNC router chatter, and how do I actually fix it?

Chatter is a self-reinforcing vibration between the cutter, workpiece, spindle, and machine structure; it leaves ripples, noise, poor finish, and shortened tool life. Start with rigidity: clamp the stock firmly, shorten cutter stick-out, check collet and bearings, and use the largest practical tool diameter. Then change one cutting variable at a time—spindle speed, feed, radial engagement, or depth—because a different RPM can move the cut into a stable zone rather than simply making everything slower.