The increased use of radiofrequency (RF) fields above 6 GHz, particularly for the 5 G mobile phone network, has given rise to public concern about any possible adverse effects to human health. Public exposure to RF fields from 5 G and other sources is below the human exposure limits specified by the International Commission on Non-Ionizing Radiation Protection (ICNIRP). This state-of-the science review examined the research into the biological and health effects of RF fields above 6 GHz at exposure levels below the ICNIRP occupational limits. The review included 107 experimental studies that investigated various bioeffects including genotoxicity, cell proliferation, gene expression, cell signalling, membrane function and other effects. Reported bioeffects were generally not independently replicated and the majority of the studies employed low quality methods of exposure assessment and control. Effects due to heating from high RF energy deposition cannot be excluded from many of the results. The review also included 31 epidemiological studies that investigated exposure to radar, which uses RF fields above 6 GHz similar to 5 G. The epidemiological studies showed little evidence of health effects including cancer at different sites, effects on reproduction and other diseases. This review showed no confirmed evidence that low-level RF fields above 6 GHz such as those used by the 5 G network are hazardous to human health. Future experimental studies should improve the experimental design with particular attention to dosimetry and temperature control. Future epidemiological studies should continue to monitor long-term health effects in the population related to wireless telecommunications.