They have found problems with studies. The National Institute of Health is doing another study.

The studies have been published in peer-reviewed journals, and the particularly valuable studies used in developing the standards have been replicated by other researchers. 

The National Institute of Health published its study on cell phones in 2001 and summarizes its major finding as follows:
“There was no indication of higher brain tumor risk among persons who had used hand-held cellular phones compared to those who had not used them.  More importantly, there was no evidence of increasing risk with increasing years of use or average minutes of use per day, nor did brain tumors among cellular phone users tend to occur more often than expected on the side of the head on which the person reported using their phone. Specifically, there was no indication of increased risk associated with use of a cell phone for one hour or more per day, for five or more years, or for cumulative use of more than 100 hours.  These findings pertain to all three tumor types considered (glioma, meningioma, and acoustic neuroma).”