Air travel during the COVID-19 pandemic is challenging for travellers, airlines, airports, health authorities, and governments. We reviewed multiple aspects of COVID peri-pandemic air travel, including data on traveller numbers, peri-flight prevention, and testing recommendations and in-flight SARS-CoV-2 transmission, photo-epidemiology of mask use, the pausing of air travel to mass gathering events, and quarantine measures and their effectiveness. Flights are reduced by 43% compared to 2019. Hygiene measures, mask use, and distancing are effective, while temperature screening has been shown to be unreliable. Although the risk of in-flight transmission is considered to be very low, estimated at one case per 27 million travellers, confirmed in-flight cases have been published. Some models exist and predict minimal risk but fail to consider human behavior and airline procedures variations. Despite aircraft high-efficiency filtering, there is some evidence that passengers within two rows of an index case are at higher risk. Air travel to mass gatherings should be avoided. Antigen testing is useful but impaired by time lag to results. Widespread application of solutions such as saliva-based, rapid testing or even detection with the help of "sniffer dogs" might be the way forward. The "traffic light system" for traveling, recently introduced by the Council of the European Union is a first step towards normalization of air travel. Quarantine of travellers may delay introduction or re-introduction of the virus, or may delay the peak of transmission, but the effect is small and there is limited evidence. New protocols detailing on-arrival, rapid testing and tracing are indicated to ensure that restricted movement is pragmatically implemented. Guidelines from airlines are non-transparent. Most airlines disinfect their flights and enforce wearing masks and social distancing to a certain degree. A layered approach of non-pharmaceutical interventions, screening and testing procedures, implementation and adherence to distancing, hygiene measures and mask use at airports, in-flight and throughout the entire journey together with pragmatic post-flight testing and tracing are all effective measures that can be implemented. Ongoing research and systematic review are indicated to provide evidence on the utility of preventive measures and to help answer the question "is it safe to fly?".