One of the most robust animal studies in the world comes from the US government. In 1999, during the Clinton administration, the Food and Drug Administration asked the National Toxicology Program (NTP) to study the toxicity and cancer-causing capability of cellphone radio-frequency radiation. At the time, health officials felt epidemiological studies in humans wouldn’t answer these questions, so the NTP embarked on studies in rats and mice.

Experts consulted by France considered it was mandatory that the main antenna axis should not to be directly in front of a living place at a distance shorter than 100 metres.[22] This recommendation was modified in 2003[23] to say that antennas located within a 100-metre radius of primary schools or childcare facilities should be better integrated into the cityscape and was not included in a 2005 expert report.[24] The Agence française de sécurité sanitaire environnementale (fr) as of 2009, says that there is no demonstrated short-term effect of electromagnetic fields on health, but that there are open questions for long-term effects, and that it is easy to reduce exposure via technological improvements.[25]

In this frequency range, the interaction between matter and light is via the electric field component of light (totally different from how ionizing radiation messes you up). In particular, an oscillating electric field causes polar molecules to rotate or attempt to rotate, and the lag between the applied field and the response of the molecules manifests as dissipation—i.e. heating [3]. This is the same dielectric heating which is the operating principle behind microwave ovens (which operate at 2450 MHz [4] similar to wifi). So if cell phones were to cause damage to tissue, the mechanism would be the same as what happens in a microwave oven—boiling the water in your head/body.

Epidemiology studies investigating cell phone use patterns with human cancer risk have produced inconsistent results. Some studies enrolled people who already had tumors with suspected links to RF radiation, such as gliomas, acoustic neuromas and salivary gland tumors. Researchers compared the self-reported cell phone use habits of the cancer patients with those of other people who did not have the same diseases. Other studies enrolled people while they were still healthy, and then followed them over time to see if new cancer diagnoses tracked with how they used cell phones. All the epidemiology studies, however, have troubling limitations, including that enrolled subjects often do not report their cell phone use habits accurately on questionnaires.

But not everyone is unconcerned. In May 2015, a group of 190 independent scientists from 39 countries, who in total have written more than 2,000 papers on the topic, called on the United Nations, the World Health Organization, and national governments to develop stricter controls on cell-phone radiation. They point to growing research—as well as the classification of cell-phone radiation as a possible carcinogen in 2011 by the International Agency for Research on Cancer, part of the WHO—suggesting that the low levels of radiation from cell phones could have potentially cancer-causing effects.
“The exposures used in the studies cannot be compared directly to the exposure that humans experience when using a cell phone,” John Bucher, a senior scientist at the NTP, a government program within the department of Health and Human Services, says in a press release. “In our studies, rats and mice received radio frequency radiation across their whole bodies. By contrast, people are mostly exposed in specific local tissues close to where they hold the phone. In addition, the exposure levels and durations in our studies were greater than what people experience.”

In 2007, Dr Devra Davis founded non­profit Environmental Health Trust to provide basic research and education about environmental health hazards. Dr Davis served as the President Clinton appointee to the Chemical Safety and Hazard Investigation Board in the U.S.A. from 1994–­1999, an independent executive branch agency that investigates, prevents and mitigates chemical accidents.
The Ministry of Health Medical Administration circular (from 2002) addressed to hospital Directors, states that use of mobile phones and wireless handheld transceivers (walkie talkie) in the hospital, must on the one hand guarantee the patient’s wellbeing and safety, and on the other hand, allow the staff, the patients and their families to enjoy the service benefits. This circular outlines the areas where use of mobile phones is strictly forbidden and areas where use is permitted (while keeping an appropriate safety distance from areas where life-supporting equipment or systems are operated).
A phone's specific absorption rate (SAR) reveals the maximum amount of radiation the human body absorbs from the phone while it's transmitting. SAR testing ensures that the devices sold in the U.S. comply with the Federal Communications Commission (FCC) SAR exposure limit, but the single, worst-case value obtained from this SAR testing is not necessarily representative of the absorption during actual use, and therefore it is not recommended for comparisons among phones. In short, selecting a lower SAR phone will not reliably ensure lower radiation absorption during use. The FCC has more information at Specific Absorption Rate (SAR) For Cell Phones: What It Means For You.
The papers found that, in male rats, there was “clear evidence” that exposure to cell phone radiation increased risk for a rare type of malignant tumor called schwannoma in the connective tissues that surround nerves in the heart (they found “equivocal” evidence for the same thing in female rats). They also found “some evidence” that the radiation caused malignant glioma—a type of brain cancer affecting glial cells—in the male rats.
Pong’s claims for its case have stood up to the scrutiny of Wired magazine and the Better Business Bureau (Advertising Self-Regulation Council 2012; Ganapati 2009). In tests conducted by Cetecom, a cell phone radiation certification lab, and observed by a reporter from Wired magazine, an iPhone 3G tested without a case had a maximum SAR of 1.18 W/kg when held at the ear. The same phone tested with a Pong case had a maximum SAR of 0.42 W/kg (Ganapati 2009).  
There is no strong or consistent evidence that mobile phone use increases the risk of getting brain cancer or other head tumors. The United States National Cancer Institute points out that "Radiofrequency energy, unlike ionizing radiation, does not cause DNA damage that can lead to cancer. Its only consistently observed biological effect in humans is tissue heating. In animal studies, it has not been found to cause cancer or to enhance the cancer-causing effects of known chemical carcinogens." The majority of human studies have failed to find a link between cell phone use and cancer. In 2011 a World Health Organization working group classified cell phone use as "possibly carcinogenic to humans". The CDC states that no scientific evidence definitively answers whether cell phone use causes cancer.[5][7][8]

The recent study [5] about cell phones causing cancer in rats should be taken with a grain of salt when making the connection to humans [6]. In particular, the rats in the study were exposed to radiation power densities of 0, 1.5, 3, or 6 W/kg (see p 7 in ref. 4 below). This would be equivalent of the 100 kg human getting up to 600 Watts — basically getting microwaved. As discussed earlier, cell phones are hundreds of times weaker.
Researchers have carried out several types of epidemiologic studies in humans to investigate the possibility of a relationship between cell phone use and the risk of malignant (cancerous) brain tumors, such as gliomas, as well as benign (noncancerous) tumors, such as acoustic neuroma (tumors in the cells of the nerve responsible for hearing that are also known as vestibular schwannomas), meningiomas (usually benign tumors in the membranes that cover and protect the brain and spinal cord), and parotid gland tumors (tumors in the salivary glands) (3).