Most mobile phones work in the microwave area of the radio spectrum. This region is also used by some TV transmitters, baby monitors, radar, Global Positioning Systems, 'wifi hotspots', police speed traps, garage door controls, car central-locking systems and microwave ovens.
After an extensive record of research going back several decades, it remains that there are "no known health affects below (existing emission) limits" (World Health Organization presentation, 2004). This has been reinforced by several independent health science reviews carried out around the world in the last few years.