Inhaling the fumes can cause health problems, such as allergy.
I've used a table-top fan directed away from the soldering iron, so it pulls the fumes out of my face. I've also used a rechargeable hand held vacuum cleaner to suck the fumes. (The batteries run flat quickly and vacuum cleaners make noise.)
Depending on the weather and air pressures, keeping a window or door open near where you solder can help. But sometimes the airflow comes inside instead of going outside.
Some fluxes are more poisonous, allergenic or irritating than others, and if you will use extra flux (from syringe, flux pen or other form) you will probably experience stronger fumes, which are best to be ventilated somewhere else from the house.
