One major source of controversy related to possible health effects of radiofrequency radiation (RFR) is the large number of reported statistically significant effects of exposure, over the entire RF part of the spectrum and over a wide range of exposure levels, even as health agencies do not find clear evidence for health hazards of exposure at levels within current IEEE and ICNIRP exposure limits. This Perspective considers 31 studies related to genetic damage produced by exposure to RFR at frequencies above 6 GHz, including at millimeter-wave (mm-wave) frequencies. Collectively, the papers report many statistically significant effects related to genetic damage, many at exposure levels below current exposure limits. However, application of five risk of bias (RoB) criteria and other considerations suggest that the studies in many cases are vulnerable to false discovery (nonreplicable results). The authors call for improvements in study design, analysis and reporting in future bioeffects research to provide more reliable information for health agencies and regulatory decision makers. This Perspective is a companion to another Perspective by Mattsson et al. elsewhere in this volume (Mattsson et al., 2021)1.