There are circulating rumors striking fear in the hearts of smartphone consumers where placing one's mobile phone close to yourself would “mutate cells into unstoppable reproduction” and give you cancer. Such wild claims may be validated if it meets certain criteria and probability is accounted for. But one is eventually exposed to cancerous risks in the long run. All living things are continuously exposed to radiation from natural causes and there is little that can be done about it, unless spending the rest of one's life sheathed in lead coating becomes a viable option. But it also doesn't entail a lost battle, nor does it recommend turning a blind eye on other potential risks. Our species is living in a world governed by entropy (religion aside). Everything that occurs is highly probabilistic, existence being a game of chance. In spite of an unforeseeable future, we can make the odds turn in our favor though, in as much as the probability of the other event happening becomes infinitesimal. For this reason, certain regulations specified by the international telecommunications union (ITU), the federal communications commission (FCC), and other governing telecommunications entities were established. (For example, only phones with maximum Specific Absorption Rate SAR levels of 1.6 watts per kilogram can be sold in the United States)

Before anything else, what's actually being emitted by cellphones and routers? Analog modulated digital signals in the form of electromagnetic (EM) waves are propagated by 2 antennas (for mobile communications devices employing space diversity). These EM waves are the same waves that compose light, infrared, x-rays, and cosmic rays; each primarily distinguished by frequency. The frequency used by mobile phones typically lay at the Gigahertz range (10^9 Hertz), all lower frequencies being utilized in other applications. Above Gigahertz frequencies (in ascending order) are  infrared, light, x-rays, and cosmic rays. These EM waves possess energy quantified by E=hf, where h is Planck's constant and f is the frequency of the radiating particle (photon for light). From the equation, it is easily established that energy increases with frequency, implying that x-rays and cosmic rays are the EM waves with peak energy density, making them dangerous and carcinogenic. 

Because of Einstein's theory on the photoelectric effect, where it was observed that increasing the magnitude of EM waves does not increase effectiveness in releasing free electrons from metals, smartphone consumers consequently are not at risk when exposed to very high power radio waves. The story changes however, when the footprint of the antenna and duration of exposure is accounted for. The near field has an energy density much much higher than the far field, thus one should avoid sticking electronics that are incessantly transmitting EM signals too close to themselves. The near field range is very short though, approximately 2 inches with a broadband USB stick. As for exposure, it follows that longer exposure leads to higher risk of developing cancer.

The probability of cancer risk from smartphones is small. So small that the probability is the same as that of getting cancer from natural occurring sources. This probability can increase or decrease based on the way mobile handsets are handled. It is up to the user to take care in minimizing such chances.