This article reviews, at a nontechnical level, the issue of potential health effects of millimeter wave exposure (30-300 GHz) as well as 5G NR exposure in the high band (presently, 24.25-52.6 GHz). MM-wave energy is chiefly absorbed in the top layers of skin. The established hazards from such energy are associated with excessive heating of tissue, including thermal damage to skin and the eye, and thermal pain. Present exposure limits to mm-waves in IEEE Standard C95.1-2019 and ICNIRP (2020) Guidelines are based on numerical modeling of tissue heating and on a limited number of human and animal studies, and appear to be quite conservative with respect to thermal hazards. The existence of many mm-wave bioeffects studies, many reporting biological effects of exposure over a wide range of frequencies and exposure levels but with high risk of bias and other limitations, introduces significant uncertainty in assessing the health effects literature. Health agencies have not identified hazards of 5G high band and mm-wave exposure at "nonthermal" levels below current exposure limits, but all recommend further research. The present authors suggest several lines of needed research, and point to the need to improve the quality of future bioeffects studies.