Most concerns focus around the electromagnetic radiation heating your tissue. Microwave ovens operate at 2.4MHz, and most common frequencies can work like a microwave with varying efficiency. At the intensities of normal transmissions that isn't really a concern. For a time this seemed like something we might worry about with phones, since during a phone call there we have an active antenna right next to your fairly sensitive brain that might not like being heated up. But even there it turned out that the effect was too small to be of concern
Ham radio operators do need to worry about radio exposure safety for heating. But we are using much higher powers, 100W is normal HF radio, and 1500W is the limit. 5W handheld next to head is safe. Also, the
“DNA Breathing Dynamics in the Presence of a Terahertz Field” by B. S. Alexandrov, V. Gelev, A. R. Bishop, A. Usheva, K. O. Rasmussen (Submitted on 28 Oct 2009)
"Abstract: We consider the influence of a terahertz field on the breathing dynamics of double-stranded DNA. We model the spontaneous formation of spatially localized openings of a damped and driven DNA chain, and find that linear instabilities lead to dynamic dimerization, while true local strand separations require a threshold amplitude mechanism. Based on our results we argue that a specific terahertz radiation exposure may significantly affect the natural dynamics of DNA, and thereby influence intricate molecular processes involved in gene expression and DNA replication."
The book "The Body Electric: Electromagnetism And The Foundation Of Life"
by Robert Becker and Gary Selden, is a foundational book for this research. First published in 1998.
Becker in his research found that lower power levels could have biological effects, everything else being equal, than higher power levels.