Cell phones use radiofrequency (RF) wave (600-3000 MHz) to exchange information. This RF radiation is non-ionizing, that is, the signal would not kick the electrons out of atoms. One can confirm it by just simply calculating the maximum energy of the photon of RF waves:
On the other hand, the power of these RF waves is low. For example, the peak total radiated power (TRP) of Global System for Mobile Communications (GSM) phones is 33 dBm (900 MHz channel) or 30dBm (1800 MHz channel), where the unit dBm is the decibels relative to the power unit milliwatt.  So the standard peak TRP of GSM phones is 103.3 × 1 mW = 2 W (900MHz), or 103.0 × 1 mW = 1W (1800MHz). This power is much lower than some common radiations such as solar light (solar constant ∼103 W/m2). But, are they really safe?
Although RF waves are non-ionizing, their electric field can also polarize the molecules in human body, so the tissue near a communicating cell phone would absorb the power of the RF signal. Krogenus et al. showed that the peak TRP would drop from 28.0 dBm (without human body) to 23.8 dBm if people hold the cell phone with hand and attach it to the head.  So human body would absorb
of the radiofrequency signal. Specific Absorption Rate (SAR) is often used to indicate the strength of exposure of RF waves. The definition of SAR is the power of absorbed RF wave per unit mass of tissue. IEEE standards recommend the safe peak exposure rate of public should be less than 0.08 W/kg. 
For a GSM cell phone using a 900 MHz channel, the peak SAR of the user (assuming the weight is 60 kg) should be
which is safe according to the IEEE standards. But actually this is an average over the whole body; and the peak SAR of the tissue around the cell phone should be much higher than that value.
One effect of cell phone radiation is heat. The alternating electric field would drive the electrons in the molecules to oscillate; and the kinetic energy of the oscillation would dissipate into heat and then increase the temperature of the tissue. If that temperature is too high, it would damage the tissue itself. The threshold ΔT of damaging brain/eye tissue is about 4 °C (continue for 30 minutes).  Bernadi et al. found there is a significant increase of body temperature around a cell phone with 600 mW peak TRP.  They detected that the temperature of the ear increases 0.22∼0.43 °C after a 20-minute continuous using of cell phone, with a 2 W/kg SAR (averaged over 1 g of the tissue); and the temperature of the brain increases 0.09∼0.19 °C, with a 1 W/kg SAR (averaged over 1 g of the tissue). On the other hand, V. Anderson et al. found the eye temperature increases 0.022 °C with an SAR of 0.21 W/kg, also using a 600 mW cell phone.  Assuming the temperature increase is proportional to the peak TRP, the temperature increase of human brain would be about 0.5°C if GSM 900 Hz channel is used. And this should be safe according to. 
Other effects of RF waves on human body are still not very clear. Some researches show radiofrequency wave can affect the activities of human organs and cells, and even chromosomes. Volkow et al. showed the metabolism rate of brain becomes significantly higher when people are using cell phones (the rate of glucose metabolism increases from 33.3 to 35.7 μmol/100 g per minute).  Huber et al. reported 900 MHz RF wave with a peak SAR 1 W/kg can affect the regional cerebral blood flow (rCBF).  After a 20-min exposure of RF wave on the left-hand side, the rCBF of the left and right hemisphere of the brain becomes 4.3:0.4. Andrzejak et al. showed during a 20-minutes telephone call with a GSM phone, the standard deviation of human heart rate increases from 74 ms (without cellphones) to 92 ms.  J. Miyakoshi et al. showed the treatment of Human Glioma Cells with a 1950 MHz RF field may inhibit the phosphorylation (an important chemical process) of Hsp27 at Serine78 in MO54 cells.  Mashevich et al. used 830 MHz electromagnetic fields to treat human peripheral blood lymphocytes (some cells in human body), and found losses and gains of chromosomes increase linearly as the SAR increases from 1.6 to 8.8 W/kg.
However, it seems that no obvious evidence shows RF wave would cause any diseases. Sommer et al. showed radiofrequency waves cannot affect the reproduction system of mice even with a very strong field (22 W/m2) in several generations.  M.H. Repacholi et al. investigated hundreds of studies and concluded that for adults, there is no consistent relation between cell phone using and head tumors.  D. Aydin et al. also showed there is no increasing risk of getting cancer for children and adolescents cell phone users.  E. D. Kirson et al. even reported that the electromagnetic field with certain frequency (100 to 300 kHz) can destroy cancer cells selectively. 
So far, there are many studies on the danger of RF waves, but no definite conclusion can be made according to these studies. That cell phones can be harmful to human health is just a possibility: it is reported that the WHO considers cell phone radiation as "possibly carcinogenic."  Nevertheless, without knowing the mechanism of how RF waves affect human body, it is impossible to answer this question reasonably.
© Di Lu. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
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