Non-ionizing radio-frequency (RF) radiation, the kind used in wireless devices, is presumed safe due to the popular conception of how light can damage cells: by ionizing DNA strands or other key molecules. If RF radiation is too low-frequency to be able to ionize an atom inside a cell, then it is assumed to be completely safe. Major health bodies, like the International Agency for Research on Cancer, have not yet classified RF radiation as a health hazard because the last time that this matter was considered, 2011, the evidence was scarce and what little evidence there was was unconvincing.
At that time, it was understood that RF radiation could have a thermal effect on biological tissue, similar to a microwave, and so the IARC classified RF as a Group 2B carcinogen (Possibly Carcinogenic to Humans).
Since 2011, much more evidence has been developed, and multiple meta-analyses have concluded that RF radiation should reasonably be reclassified into Group 1 (Carcinogenic to Humans).
See Studies.