The goal of this article is to demonstrate the value of a global perspective on pandemics for understanding how global pandemics caused by novel viruses can unfold. Using the example of the 1918 influenza pandemic, two factors that were central to the evolving pattern of global pandemic waves, connectivity and seasonality, are explored. Examples of the influences of these factors on pandemic waves in different locations are presented. Viewing the 1918 pandemic through the lens of compartmental models of infectious diseases, our analysis suggests that connectivity played a dominant role in the initial stages. With the passage of time and the progressive infection and consequent immunization of more and more people, however, the role of seasonality increased in importance, ultimately becoming the driving force behind the emergence of future waves of infection. Implications of these observations for pandemics caused by novel viruses such as the ongoing COVID-19 pandemic are discussed.