Transmissions allow engines to operate at optimal RPM for efficiency using gear ratios to reduce RPM and multiply torque. They contain gears that change the speed and direction of rotation. Planetary gears, common in automatic transmissions, use three components - sun gear, planet gears, and ring gear. By holding one component and driving another, different gear ratios are achieved like underdrive, overdrive, and reverse. Ratios are calculated using the number of teeth on each component.