The year 2020 is witnessing a global health and economic crisis due to the COVID-19 pandemic. Countries across the world are using digital technologies to fight this global crisis. These digital technologies strongly rely, in one way or another, on the availability of wireless communication systems. This paper aims to outline the role of wireless communications in the COVID-19 pandemic from multiple perspectives. First, we show how wireless communication technologies are helping to combat this pandemic by monitoring the spread of the virus, enabling healthcare automation, and enabling virtual education and conferencing. We emphasize the importance of digital inclusiveness in the pandemic and possible solutions to connect the unconnected. Next, we discuss the challenges posed by the use of wireless technologies, including concerns about privacy, security, and misinformation. Later, we highlight the importance of wireless technologies in the survival of the global economy, such as automation of industries and supply chain, e-commerce, and supporting occupations that are at risk. Finally, we outline that the rapid development of wireless technologies during the pandemic is likely to be useful in the post-pandemic era.