When cellphone technology began widespread deployment in 1984 the only criteria recognized for RF safety was that of thermal heating of tissue. Lured by the convenience that would be afforded by communicating freely and the assertion by industry
representatives that such phones were of insufficient power to cause heating, federal authorities exempted cellphones from premarket testing. Triggered by a 1993 death of a woman from an epithelial brain tumor, a rare cancer that grows from the outside in, that was located where the antenna of her cell phone was when she used it, the Cellular Telephone Industry Association (CTIA - The Wireless Association) paid to do its own big cancer study in the 1990s - provided the FCC would not regulate them - until the study was done. But by 1998 researchers were finding the signals caused leakage in the blood-brain barrier that allows dangerous heavy metals and other chemicals to enter the highly sensitive brain. Micronuclei were also found in blood cells. These micronuclei had also been found in patients exposed to fallout from the 1989 Chernobyl nuclear accident and are linked to cancer. 
Congress had a hearing on health consequences of cell phone use in 2009. 
Yet even with compelling evidence of harm from expert testimony [521a] the FDA removed all such concerns from its website. [521b] The number of active cell phones was to exceed the human population, reaching 7.3 billion by 2014.  While the use of cellphones, cordless phones and/or WiFi devices is voluntary and intermittent - and that from newer cellphones has even been shown to be less than that from their older counterparts there are studies on the effects of the microwave and near-microwave energy from these devices to be aware of.
In 2011 the WHO designated the wireless radiation from cellphones as a Class 2B,
possible human carcinogen.  The National Institutes of Health (NIH) described cellphone use of less than an hour per day as changing brain activity.  Full peer-reviewed report here: [523a] Studies carried out in Sweden indicate that those who begin using either cordless or mobile phones regularly before age 20 have greater than a fourfold increased risk of ipsilateral (side of head where phone is held) glioma.  A 2012 study shows 290% increase in malignant brain tumors with >10 years of cell phone use and 450% increase with >10 years cordless phone use. [524a]And a Russian meta study shows that because of oxidative effects of low-intensity radiofrequency radiation (RFR) on living cells using a cell phone for just 20 minutes a day for five years increases the risk of one type of brain tumor threefold, and using the phone an hour a day for four years upped the risk of some tumors three to five times, according to the author. [524b], [524c]
This contradicts the findings of the International Agency for Research on Cancer on the Interphone Study  done in Australia, Canada, Denmark, Finland, France, Germany, Israel, Italy, Japan, New Zealand, Norway, Sweden and the UK in the late 90s that found no connection between cellphone use and brain cancer over a ten year period and concluded that “The possible effects of long‐term heavy use of mobile phones require further investigation.”  But Israeli participants were found to clearly indicate a link between cellphone use for more than 10 years and the development of tumors in the salivary glands, particularly among people who held the telephone on the same side where the tumor developed and individuals in the highest category of exposure (heavy use in rural areas). 
In June, 2014, Berkeley, CA unanimously passed an historic cellphone right to know ordinance. A Harvard Law Professor offered his services pro-bono to put forth a bullet-proof ordinance. Folks in Berkeley will now be handed safety information every time they purchase a cell phone. (It’s not as safe as using only hard-wired or fiber optic technology, but at least folks will know this technology is dangerous and keep devices off their bodies.) ,[528a]
Studies reveal that using a cell phone for 10 years or longer for a half-hour a day can double the risk of glioma or acoustic neuroma (brain tumors) on the same ("ipsilateral") side of the head as that preferred for cell phone use. ,[529a] Cancer risk is three times higher for those having used cellphones for 25 years or more. ,[531a] A 2013 study reviewed data on those having used 2G or 3G digital phones from one to 5 years from 2007-2009 concluded IARC's 2011 designation of RF-EMF as a Class 2B possible human carcinogen should be upgraded to 2A probable human carcinogen. 
Legislative Safety Measures
While the British government finds no cancer risks associated with cell phone use, it recommends precautions including keeping calls short and minimal use for children to essential calls only. [531b] EPA also suggests keeping calls short; using hands-free air-tube earphones to keep the phone away from your head; and increasing distance between your body and the phone when not in use as precautions. [531c]
The school environment has a high concentration of RFR. 90% of students now have cellphones and many schools have upgraded their networks to wireless. Cell phone use is now banned in 1/3rd of British schools and it has been found that grades have improved by 6% in those schools along with decreased behavioral problems. 
Berkeley, CA passed a Right to Know ordinance that requires labeling or info be provided to buyers of cell phones there.  This has been upheld in court.
Protect Yourself & Others
When using a cellphone or any wireless device remember that distance is your friend. If you need to be near the phone then keep it in the room a few feet away, NOT anywhere on your body! A phone in a man's pocket can affect sperm motility while a phone in a woman's bra can promote breast cancer. Use the phone on speaker, if that's comfortable or practical for you or try using an airtube headset.
On the go, avoid using phone in weak-signal areas as it must transmit higher power RF signal to communicate with the tower. Same thing, inside cars, elevators, busses and trains: Metal walls make phone work harder to maintain link to tower and can reflect much of the RF signal within the space and back to you instead of out to the tower.
Here are some safety tips for minimizing RF exposure while using a cell phone.