When you talk, your voice is transmitted from the antenna as radio frequency radiation (RFR) between 800 MHz and 2,200 MHz. A range equal to the middle of microwave frequency and 20% to 80% of the radiation emitted is deposited in the user's head. The microwave radiation is absorbed and penetrates the area around the head, some reaching an inch, to an inch and a half into the brain. Exposure to this microwave RFR has shown to have serious health consequences. Laboratory studies have shown that radiation from cell phones expose the user to a wide range of health problems including: 

The reason we’re talking about cellphones and cancer — why there’s a concern here — is because they emit radiation, the invisible waves of electric and magnetic energy, of varying power, organized on the electromagnetic spectrum. You can see in the graphic below that less powerful (or lower-frequency) types of radiation are on the left, moving to the more powerful (or higher-frequency) types of radiation on the right.
In 2015, the European Commission Scientific Committee on Emerging and Newly Identified Health Risks concluded that, overall, the epidemiologic studies on cell phone radiofrequency electromagnetic radiation exposure do not show an increased risk of brain tumors or of other cancers of the head and neck region (2). The Committee also stated that epidemiologic studies do not indicate increased risk for other malignant diseases, including childhood cancer (2).

The energy of electromagnetic radiation is determined by its frequency; ionizing radiation is high frequency, and therefore high energy, whereas non-ionizing radiation is low frequency, and therefore low energy. The NCI fact sheet Electromagnetic Fields and Cancer lists sources of radiofrequency radiation. More information about ionizing radiation can be found on the Radiation page.