How do microwaves affect our brains? Do radio waves have the same effect?

Microwaves are part of the electromagnetic spectrum, with a higher frequency than, say, VHF radio waves, but less than infra-red or even visible light. Their ability to heat things - as seen in microwave ovens - comes because their comparatively long wavelength lets them penetrate materials which are opaque to the shorter waves of visible light. Hence you can "microwave" food enclosed in a cardboard box.

That is fine in a microwave oven, but worrying in a hand-held communications device, because the nearest body part to the aerial is the watery tissue of the brain. Water is especially good at absorbing microwave radiation, which is why it's good for cooking - but domestic ovens contain failsafe switches to stop you putting your hand in while the power is on.