The reason we’re talking about cellphones and cancer — why there’s a concern here — is because they emit radiation, the invisible waves of electric and magnetic energy, of varying power, organized on the electromagnetic spectrum. You can see in the graphic below that less powerful (or lower-frequency) types of radiation are on the left, moving to the more powerful (or higher-frequency) types of radiation on the right.
That’s because cell phones emit electromagnetic fields (EMFs) or electromagnetic radiation, which has the potential to damage the cells in the body. In fact, the International Agency for Research on Cancer classifies EMFs from cell phones as possible carcinogens. EMFs can interfere with the body’s natural electrical system and disrupt sleep, immune system function, hormone production, and the healing process. Kevin Byrne, president of EMF Solutions, also points out the simultaneous increase in conditions such as chronic pain, depression, anxiety, chronic fatigue syndrome, and Alzheimer’s disease and the significant rise in EMF exposure.

Specific Absorption Rate (SAR) is an indicator for calculating the level of radiation absorbed in the body. This indicator represents the rate of energy absorption by the tissue and is expressed in units of Watt/kg. The Consumer Protection Regulations (information on non-ionizing radiation from mobile phones) of 2002, stipulate the duty to label the product, specifying the radiation level of the phone’s model and the maximum permitted radiation level. This regulation allows to compare the emitted radiation level between different instruments and to take this into consideration when weighing the factors determining the choice of a new instrument at the time of its purchase.

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.
But, like the human studies, one can pick apart the NTP studies too. For one thing, the animals experienced cell phone radiation that was different from what humans live with. As Bucher said in a statement, “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.”
Specifically, we looked for studies that measured rates of acoustic neuromas, gliomas, meningiomas, and thyroid cancers. We also narrowed our search to studies that looked at the effect of radio-frequency radiation originating from an actual cellphone, rather than experimental equipment. We did this because we wanted evidence that could apply to real life, not specific laboratory settings or hypothetical outcomes.
EWG believes that cell phone testing procedures should include cases and other accessories, whether supplied by the phone manufacturer or a third party. Since these cases and accessories have no other use and have the potential to influence the phone’s transmitting and receiving activity and the amount of radiation that a user might encounter, they fall within FCC’s authority.

The company's "Researches" page, for example, states that "Aires Technologies are more than 12 years (sic). For this period there have been conducted a number of studies on mechanisms of coherent transformers that effect on physical, chemical, technological and biological processes (sic). The studies were carried out in close collaboration with leading research and academic institutions."
The only consistently recognized biological effect of radiofrequency radiation in humans is heating. The ability of microwave ovens to heat food is one example of this effect of radiofrequency radiation. Radiofrequency exposure from cell phone use does cause heating to the area of the body where a cell phone or other device is held (e.g., the ear and head). However, it is not sufficient to measurably increase body temperature. There are no other clearly established effects on the human body from radiofrequency radiation.