Computational intelligence has been used in many applications in the fields of health sciences and epidemiology. In particular, owing to the sudden and massive spread of COVID-19, many researchers around the globe have devoted intensive efforts into the development of computational intelligence methods and systems for combating the pandemic. Although there have been more than 200,000 scholarly articles on COVID-19, SARS-CoV-2, and other related coronaviruses, these articles did not specifically address in-depth the key issues for applying computational intelligence to combat COVID-19. Hence, it would be exhausting to filter and summarize those studies conducted in the field of computational intelligence from such a large number of articles. Such inconvenience has hindered the development of effective computational intelligence technologies for fighting COVID-19. To fill this gap, this survey focuses on categorizing and reviewing the current progress of computational intelligence for fighting this serious disease. In this survey, we aim to assemble and summarize the latest developments and insights in transforming computational intelligence approaches, such as machine learning, evolutionary computation, soft computing, and big data analytics, into practical applications for fighting COVID-19. We also explore some potential research issues on computational intelligence for defeating the pandemic.