It is very exceptional that a new disease becomes a true pandemic. Since its emergence in Wuhan, China, in late 2019, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes COVID-19, has spread to nearly all countries of the world in only a few months. However, in different countries, the COVID-19 epidemic takes variable shapes and forms in how it affects communities. Until now, the insights gained on COVID-19 have been largely dominated by the COVID-19 epidemics and the lockdowns in China, Europe and the USA. But this variety of global trajectories is little described, analysed or understood. In only a few months, an enormous amount of scientific evidence on SARS-CoV-2 and COVID-19 has been uncovered (knowns). But important knowledge gaps remain (unknowns). Learning from the variety of ways the COVID-19 epidemic is unfolding across the globe can potentially contribute to solving the COVID-19 puzzle. This paper tries to make sense of this variability-by exploring the important role that context plays in these different COVID-19 epidemics; by comparing COVID-19 epidemics with other respiratory diseases, including other coronaviruses that circulate continuously; and by highlighting the critical unknowns and uncertainties that remain. These unknowns and uncertainties require a deeper understanding of the variable trajectories of COVID-19. Unravelling them will be important for discerning potential future scenarios, such as the first wave in virgin territories still untouched by COVID-19 and for future waves elsewhere.