The COVID-19 epidemic has caused a large number of human losses and havoc in the economic, social, societal, and health systems around the world. Controlling such epidemic requires understanding its characteristics and behavior, which can be identified by collecting and analyzing the related big data. Big data analytics tools play a vital role in building knowledge required in making decisions and precautionary measures. However, due to the vast amount of data available on COVID-19 from various sources, there is a need to review the roles of big data analysis in controlling the spread of COVID-19, presenting the main challenges and directions of COVID-19 data analysis, as well as providing a framework on the related existing applications and studies to facilitate future research on COVID-19 analysis. Therefore, in this paper, we conduct a literature review to highlight the contributions of several studies in the domain of COVID-19-based big data analysis. The study presents as a taxonomy several applications used to manage and control the pandemic. Moreover, this study discusses several challenges encountered when analyzing COVID-19 data. The findings of this paper suggest valuable future directions to be considered for further research and applications.