The current outbreak of COVID-19 is an unprecedented event in air transportation. This is probably the first time that global aviation contributed to the planet-wide spread of a pandemic, with casualties in over two hundred countries. As of August 23rd, 2020, the number of infected cases has topped 23 million, reportedly relating to more than 800,000 deaths worldwide. However, there is also a second side of the pandemic: it has led to an unmatched singularity in the global air transportation system. In what could be considered a highly uncoordinated, almost chaotic manner, countries have closed their borders, and people are reluctant/unable to travel due to country-specific lock-down measures. Accordingly, aviation is one of the industries that has been suffering most due to the consequences of the pandemic outbreak, despite probably being one of its largest initial drivers. In this study, we investigate the impact of COVID-19 on global air transportation at different scales, ranging from worldwide airport networks where airports are nodes and links between airports exist when direct flights exist, to international country networks where countries are contracted as nodes, and to domestic airport networks for representative countries/regions. We focus on the spatial-temporal evolutionary dynamics of COVID-19 in air transportation networks. Our study provides a comprehensive empirical analysis on the impact of the COVID-19 pandemic on aviation from a complex system perspective using network science tools.