There are ongoing worries about whether cellphones can give you cancer — especially brain cancer, since our phones spend so much time near our faces. It’s true that cell phones do emit radiation. But it’s radiofrequency radiation, which is much lower energy than the ionizing radiation you’d get from an X-ray, or, say, nuclear fallout. Ionizing radiation can cause DNA damage that can eventually lead to cancer. But the radiofrequency radiation from a cellphone doesn’t work that way — and today’s results support that.
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.