As physical entities, living cells possess structural and physical properties that enable them to withstand the physiological environment as well as mechanical stimuli occurring within and outside the body. Any deviation from these properties will not only undermine the physical integrity of the cells, but also their biological functions. As such, a quantitative study in single cell mechanics needs to be conducted. In this review, we will examine some mechanical models that have been developed to characterize mechanical responses of living cells when subjected to both transient and dynamic loads. The mechanical models include the cortical shell-liquid core (or liquid drop) models which are widely applied to suspended cells; the solid model which is generally used for adherent cells; the power-law structural damping model which is more suited for studying the dynamic behavior of adherent cells; and finally, the biphasic model which has been widely used to study musculoskeletal cell mechanics. Based upon these models, future attempts can be made to develop even more detailed and accurate mechanical models of living cells once these three factors are adequately addressed: structural heterogeneity, appropriate constitutive relations for each of the distinct subcellular regions and components, and active forces acting within the cell. More realistic mechanical models of living cells can further contribute towards the study of mechanotransduction in cells.