Several national and international agencies study different exposures and substances in the environment to determine if they can cause cancer. (Something that causes cancer or helps cancer grow is called a carcinogen.) The American Cancer Society looks to these organizations to evaluate the risks based on evidence from laboratory and human research studies.
That mystery probably stokes fears about cellphone radiation instead of soothing them, though — in part because of how we in the media cover the rare and frightening. We’ve seen the same thing with fear over nuclear power plants, according to a paper published in Science in the 1980s by psychologist Paul Slovic. “Because nuclear risks are perceived as unknown and potentially catastrophic, even small accidents will be highly publicized and may produce large ripple effects,” Slovic wrote.
Overall, the reviews of case-control studies seem to suggest there is perhaps no risk of cancer with cellphone use — unless you look at some subgroups (like people in blinded studies or people with long-term exposures). But these reviews are based on case-control studies — which are like the National Enquirer of the science world: cheap and often misleading.
However, there have been some studies that have shown that rats can develop a specific type of brain tumor, called a schwannoma, if they're subjected to prolonged radiofrequency radiation. These studies examined thousands of rats and mice, and exposed them to a variety of radiations — everything from "near-field" (which is what you get holding a phone to your ear) to "far-field" (which is what you get walking through everyone's Wi-Fi signals at Starbucks).

Radiofrequency radiation is a form of electromagnetic radiation. Electromagnetic radiation can be categorized into two types: ionizing (e.g., x-rays, radon, and cosmic rays) and non-ionizing (e.g., radiofrequency and extremely low frequency, or power frequency). Electromagnetic radiation is defined according to its wavelength and frequency, which is the number of cycles of a wave that pass a reference point per second. Electromagnetic frequencies are described in units called hertz (Hz).