The SARS-CoV-2 virus and COVID-19 disease have posed unprecedented and overwhelming challenges and opportunities to data and domain-driven modeling. This paper makes a comprehensive review of the challenges, tasks, methods, gaps and opportunities on modeling COVID-19 problems and data. It constructs a research landscape of COVID-19 modeling, and further categorizes, compares and discusses the related work on modeling COVID-19 epidemic transmission processes and dynamics, case identification and tracing, infection diagnosis and trends, medical treatments, non-pharmaceutical intervention effect, drug and vaccine development, psychological, economic and social impact, and misinformation, etc. The modeling methods involve mathematical and statistical models, domain-driven modeling by epidemiological compartmental models, medical and biomedical analysis, data-driven learning by shallow and deep machine learning, simulation systems, social science methods, and hybrid methods.
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