The unprecedented and overwhelming SARS-CoV-2 virus and COVID-19 disease significantly challenge our life and the society and economy. Many questions
emerge, a critical one is to quantify the challenges, realities, intervention effect
and influence of the pandemic. With the massive effort in modeling COVID-19, what COVID-19 issues have been modeled? what and how well have epidemiology, AI, data science, machine learning, deep learning, mathematics and social science
characterized the COVID-19 epidemic? what are the gaps and opportunities of quantifying the pandemic? Such questions involve a wide body of knowledge and
literature, unclear but important for the present and future health crisis quantification. Here, we provide a comprehensive review of the challenges, tasks, methods, progress, gaps and opportunities in relation to modeling COVID-19 processes, data, mitigation and impact. With a research landscape of COVID-19 modeling, we further categorize, summarize, compare and discuss the related methods and progress of modeling COVID-19 epidemic transmission processes and dynamics, case identification and tracing, infection diagnosis and medical treatments, nonpharmaceutical interventions and their effects, drug and vaccine development, psychological, economic and social influence and impact, and misinformation, etc. The review shows how modeling methods such as mathematical and statistical models, domain-driven modeling by epidemiological compartmental models, medical and
biomedical analysis, AI and data science in particular shallow and deep machine learning, simulation modeling, social science methods and hybrid modeling have addressed the COVID-19 challenges and what gaps and directions exist for better futures.