It'd be wrong to say that there is no evidence of harm at all. In fact, the re-classification by the IARC came about in the first place because the Working Group contributing to the Interphone study acknowledged "limited evidence" of an increase in glioma (a type of tumour, commonly found in the brain) among phone users in one of the studies. In this study, which concluded in 2004, researchers found that participating phone owners who had used their handsets for calls for more than 30-minutes a day, over a period of ten years, had an increase incidence of glioma.
That’s why randomized controlled trials (RCTs) often yield fairly clear answers about the effectiveness of treatments compared to other study designs. (Fun fact: Scottish doctor James Lind, a clinical trial pioneer, figured out that citrus fruits seemed to have an effect on scurvy using one of the earliest RCTs.) RCTs can also be used to study whether something, like cellphone radiation, can cause disease.
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.
Don’t be mislead by a common misconception started in the 90′s that wired headsets, that the headset that came with your cell phone is a safe alternative to placing a phone to your head. This is simply not true at all! Ordinary headsets use a wire to deliver sound to an electronic earpiece that can deliver electromagnetic radiation into your head directly through your ear canal.
The only consistently recognized biological effect of radiofrequency radiation in humans is heating. The ability of microwave ovens to heat food is one example of this effect of radiofrequency radiation. Radiofrequency exposure from cell phone use does cause heating to the area of the body where a cell phone or other device is held (e.g., the ear and head). However, it is not sufficient to measurably increase body temperature. There are no other clearly established effects on the human body from radiofrequency radiation.