In this frequency range, the interaction between matter and light is via the electric field component of light (totally different from how ionizing radiation messes you up). In particular, an oscillating electric field causes polar molecules to rotate or attempt to rotate, and the lag between the applied field and the response of the molecules manifests as dissipation—i.e. heating . This is the same dielectric heating which is the operating principle behind microwave ovens (which operate at 2450 MHz  similar to wifi). So if cell phones were to cause damage to tissue, the mechanism would be the same as what happens in a microwave oven—boiling the water in your head/body.
In 2011, the International Agency for Research on Cancer (IARC), a component of the World Health Organization, appointed an expert Working Group to review all available evidence on the use of cell phones. The Working Group classified cell phone use as “possibly carcinogenic to humans,” based on limited evidence from human studies, limited evidence from studies of radiofrequency radiation and cancer in rodents, and inconsistent evidence from mechanistic studies (4).
For example, cellphone manufacturers currently test these devices for compliance with FCC standards by placing them against the head, and near the torso with some separation. Just check out Apple’s iPhone manual: The company tests the specific absorption rate at a 5mm separation from the body. But if you wear your device in your pocket, you’re probably not going to have that 5mm separation, meaning you may be exposed to more radiation — perhaps enough to exceed current standards.
These expert committees determined that there are indeed gaps in the knowledge concerning the implications of exposure to this radiation, and therefore they called for further studies on the subjects and recommended to adopt the “precautionary principle". This principle adopts simple and relatively cheap means to reduce exposure to the minimum radiation levels possible with existing technology.
There’s not a lot of research on the effects of cell-phone use on children’s and teens’ health, the report acknowledges, but some studies have suggested that it may be associated with hearing loss, ringing in the ears, headaches and decreased well-being. Children who use cell phones will also have more years of exposure to RF energy over their lifetimes than people who started using them as adults, which leads some doctors to recommend added caution.