Anyone who has done a brake job has seen the cloud of dark dust that puffs out when you pull a wheel. It is fair to wonder whether brake dust is harmful. The short answer: in everyday amounts it is low-risk, but you should avoid breathing it during service. Here are the facts.
What brake dust is made of
Brake dust is the fine material worn off the pads and rotor - see what causes brake dust. Modern pads are largely non-asbestos organic, ceramic, or semi-metallic blends, and by law are being made copper-free. The dust is mostly metallic particles, friction-material bits, and iron from the rotor.
Everyday exposure is low-risk
The dust that settles on your wheels while driving poses little risk to the general public in normal amounts - it is out in the open air and you are not inhaling concentrated clouds of it. Older asbestos-containing pads were a genuine hazard, but asbestos has been phased out of modern automotive pads.
The real precaution: during a brake job
The time to be careful is when servicing brakes, when you can stir up and inhale a concentrated cloud of fine dust. Do NOT blow brake dust off with compressed air, which aerosolizes it. Instead, wet it down or wipe it with brake cleaner and a rag, wear a dust mask, and work in ventilation. This keeps fine particles out of your lungs.
Keeping dust down
If you dislike dust on your wheels, quality ceramic pads make far less of it than semi-metallic - see are ceramic pads low dust. Cleaning wheels regularly also prevents dust from etching the finish - see can brake dust corrode wheels. Choose quality pads and hardware.