Image showing inventor Dr. Martin Cooper and a prototype of the DynaTAC (aka "the brick"), the first commercial cellphone, 1973. Source: www.cbc.ca (accessed Sep. 21, 2009)
The radiation emitted by cell phones, known as radiofrequency (RF) radiation, is regulated by the Federal Communications Commission (FCC). Hundreds of millions of Americans use cell phones and many of them wonder if there are any health risks.
People who say cell phones are safe reference statements by the FCC and Food and Drug Administration (FDA) and point to peer-reviewed studies which conclude that cell phone use is not associated with an increased risk of brain tumors or the onset of other health problems. They contend there has been no increase in brain tumor rates despite hundreds of millions of people now using cell phones.
People who say cell phones are not safe cite peer-reviewed studies showing an association between cell phone use and tumor growth, DNA damage, and decreased fertility. They say cancers take 20-30 years to develop and cell phone studies have monitored periods of 10 years or less. They highlight the International Agency for Research on Cancer’s classification of cell phone radiation as a possible carcinogen.
Cell phones transmit their signals using RF wavelengths, which are part of the electromagnetic spectrum. Electromagnetic waves move (radiate) through space at the speed of light via interaction between their electric and magnetic fields and can penetrate solid objects such as cars and buildings.  Cordless phones, television, radio, and Wi-Fi also use RF radiation to transmit their signals.
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Photographs of the FCC's cell phone specific absorption rate (SAR) testing equipment. Source: "Research and Regulatory Efforts on Mobile Phone Health Issues," www.gao.gov, May 2001
The RF radiation from cell phones is contained in the low end (non-ionizing portion) of the broader electromagnetic spectrum just above radio and television RF and just below microwave RF. At high exposure levels, non-ionizing radiation can produce a thermal or heating effect (this is how microwaves heat food). Exposure to the high end (ionizing) radiation of ultra-violet light, X-rays, and Gamma rays is known to cause cancer.
On Apr. 3, 1973 the world's first portable cell phone, the DynaTAC (also known as "the brick"), was introduced in the United States by Dr. Martin Cooper at Motorola. The phone was a foot long, weighed two pounds, and cost $4,000. It was not until 1983 that the first commercial cell phone system was launched in Chicago by Ameritech Mobile Communications.
On Feb. 26, 1985 the first safety guidelines  for radio frequency (RF) radiation were enacted by the US Federal Communications Commission (FCC) to ensure that people were not exposed to dangerous "thermal effects" - levels of RF that could heat human flesh to harmful temperatures.
In 1993 concern over a possible link between brain tumors and cell phone use became a major public issue when CNN's Larry King Live show reported on David Reynard, a husband who had sued a cell phone manufacturer in a Florida US District Court for causing his wife's brain tumor. The case, Reynard v. NEC, was later rejected in 1995 by the court. 
On Aug. 7, 1996 the FCC expanded its guidelines on RF exposure with input from the Food and Drug Administration (FDA), the Environmental Protection Agency (EPA), the National Institute for Occupational Safety and Health (NIOSH), and the Occupational Safety and Health Administration (OSHA). The guidelines created a measure of the rate that body tissue absorbs RF energy during cell phone use called the specific absorption rate (SAR). The SAR for cell phone radiation was set at a maximum of 1.6 watts of energy absorbed per kilogram of body weight per cell phone call that averages 30 minutes when the cell phone is held at the ear. 
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Illustration showing an estimate of the absorption of radio frequency radiation into the brain based on age. Source: "The Case for Precaution in the Use of Cell Phones," www.environmentalhealthtrust.org, July 2008
SAR levels for cell phones sold in the US range from a low of .109 watts to the maximum of 1.6 watts. Holding a cell phone away from the body while using a wired earpiece or speaker phone lowers the amount of radiation absorbed, and text messaging, rather than talking, further lowers that amount.
The FDA and the International Association for the Wireless Telecommunications Industry (CTIA) signed a research agreement in 2000 to further investigate the health effects of cell phones. They concluded that "no association was found between exposure to radiofrequency (RF) radiation from cell phones and adverse health effects." 
In 2001 Senators Joseph Lieberman (D-CT) and Rep. Edward Markey (D-MA) commissioned the US Government Accountability Office (GAO) to compile a report on the safety of cell phones. The May 2001 GAO report, "Research and Regulatory Efforts on Mobile Phone Health Issues,"  concluded that there was no scientific evidence proving that cell phone radiation had any "adverse health effects" but that more research on the topic was needed.
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Illustration showing the electromagnetic spectrum. Source: "Research and Regulatory Efforts on Mobile Phone Health Issues," www.gao.gov, May 2001
In July of 2008 Dr. Ronald Herberman, Director of the University of Pittsburgh Cancer Institute, issued a warning to hospital faculty and staff  to decrease direct cell phone exposure to the head and body due to a possible connection between cell phone radiation and brain tumors. As a result of his warning, on Sep. 25, 2008 the US House Subcommittee on Domestic Policy of the Oversight and Government Reform Committee held a hearing on the possible link between cell phone use and tumors to learn more about the possible risks.  On Sep. 14, 2009, the US Senate Subcommittee on Labor, Health, Education, and Related Agencies of the Committee on Appropriations held a similar hearing entitled "The Health Effects of Cell Phone Use."  No further hearings were held on the matter in either the House or the Senate.
In 2008 the $148.1 billion wireless industry had over 270 million  subscribers in the US (87% of the population) who used over 2.2 trillion minutes of call time. 
On May 17, 2010 the largest study to date on cell phone radiation and brain tumor formation was released. The INTERPHONE study, a 13 country, 10 year, $25 million endeavor, found that there was no overall increase in the risk of the brain tumors glioma or meningioma among cell phone users, but also found "suggestions of an increased risk of glioma, and much less so meningioma, at the highest exposure levels.” The study concluded that the evidence was not strong enough to prove a causal link between cell phone use and the development of brain tumors. 
On June 22, 2010 the San Francisco Board of Supervisors voted 9-1 to make the city the nation’s first to require that retailers post cellphone radiation levels prominently in their stores.  On July 23, 2010, CTIA, the trade group representing the cell phone industry, sued the city of San Francisco to stop the implementation of the law,  and on Oct. 27, 2011, a federal judge struck down the San Francisco ordinance.  On May 7, 2013 San Francisco settled the lawsuit and agreed to a permanent injunction against implementation of the law. 
On Feb. 23, 2011 the first ever study showing that cell phone radiation causes biological effects in the human brain other than heating (thermal effects) was published in the Journal of the American Medical Association. The study found increased glucose metabolism in the areas of the brain closest to the cell phone antenna. 
On May 31, 2011 the International Agency for Research on Cancer (IARC) of the World Health Organization (WHO) issued a press release  announcing it had added cell phone radiation to its list of physical agents  that are "possibly carcinogenic to humans" (group 2B agents). Other group 2B agents include coffee, DDT, pickled vegetables, and lead. The classification was made after a working group of 31 scientists finished a review of previously published studies and found "limited evidence of carcinogenicity" from the radiofrequency electromagnetic fields emitted by wireless phones, radio, television, and radar.
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Image contrasting the number of minutes of cell phone use per day in the United States (blue line) with the number of new brain cancer diagnoses (red line) from 1991-2008. Source: Scott Woolley, "Cell Phone Use Is Way up. So Why Did Brain Cancer Rates Fall?," tech.fortune.cnn.com, June 7, 2011
On Oct. 20, 2011 the British Medical Journal published a study of 358,403 Danish citizens which concluded that "there was no association between tumors of the central nervous system or brain and long term (10 years +) use of mobile phones.” 
On Oct. 18, 2012 the Italian Supreme Court ruled that a causal link between cell phone use and tumor formation exists. The appellant, Innocenzo Marcolini, argued that his benign neurinoma tumor was caused by the five to six hours a day he spent talking on his cell phone for work over a 12 year period. Based on the Court opinion "that scientific evidence advanced in support of the claim was reliable," the Italian Supreme Court ruled that Marcolini was entitled to an 80% disability pension from the Italian Worker's Compensation Authority. 
On July 24, 2012 the US Government Accountability Office (GAO) released a report on exposure and testing requirements for cell phones and concluded that the FCC should "formally reassess" the effect of cell phone radiation on human health and the radiation exposure limit set by the FCC in 1996.  On Mar. 29, 2013 the FCC officially opened an inquiry on this recommendation. 
On May 26, 2016, the US National Toxicology Program (NTP) released the initial findings of its 10-year, $25 million study into whether or not radio frequency (RF) radiation from cell phones and wireless networks can cause cancer. The study found an increased incidence of malignant tumors of the brain (gliomas) and heart tumors (schwannomas) in rats exposed to RF radiation, and concluded that the tumors were "considered likely the result of whole-body exposures" to two types of RF radiation used in US cell phones and wireless networks. The findings of the study have been criticized by some researchers, including the Deputy Director of the National Institutes of Health's Office of Extramural Research, Michael Lauer, who stated in his review that he was "unable to accept the authors' conclusions." 
On Nov. 1, 2018, the NTP released its final peer-reviewed report, concluding that there is "clear evidence of carcinogenic activity" in male rats exposed to RF radiation.  However, the FDA stated in a Nov. 1, 2018 press release that they disagree "with the conclusions of their [NTP's] final report regarding 'clear evidence' of carcinogenic activity in rodents exposed to radiofrequency energy," and reiterated that "the available scientific evidence continues to not support adverse health effects in humans caused by exposures" to cellphone RF radiation. 
As of July 2018 the $475 billion wireless industry had over 400 million wireless devices in use in the United States and 323,448 cell phone tower sites across the country.