The disease caused by SARS-CoV-2-CoVID-19-is a global pandemic that has brought severe changes worldwide. Approximately 80% of the infected patients are largely asymptomatic or have mild symptoms such as fever or cough, while rest of the patients display varying degrees of severity of symptoms, with an average mortality rate of 3-4%. Severe symptoms such as pneumonia and acute respiratory distress syndrome may be caused by tissue damage, which is mostly due to aggravated and unresolved innate and adaptive immune response, often resulting from a cytokine storm. Here, we discuss how an intricate interplay among infected cells and cells of innate and adaptive immune system can lead to such diverse clinicopathological outcomes. Particularly, we discuss how the emergent nonlinear dynamics of interaction among the components of adaptive and immune system components and virally infected cells can drive different disease severity. Such minimalistic yet rigorous mathematical modeling approaches are helpful in explaining how various co-morbidity risk factors, such as age and obesity, can aggravate the severity of CoVID-19 in patients. Furthermore, such approaches can elucidate how a fine-tuned balance of infected cell killing and resolution of inflammation can lead to infection clearance, while disruptions can drive different severe phenotypes. These results can help further in a rational selection of drug combinations that can effectively balance viral clearance and minimize tissue damage.