The interplay between the mechanical properties of cells and the forces that they produce internally or that are externally applied to them play an important role in maintaining the normal function of cells. These forces also have a significant effect on the progression of mechanically related diseases. To study the mechanics of cells, a wide variety of tools have been adapted from the physical sciences. These tools have helped to elucidate the mechanical properties of cells, the nature of cellular forces, and mechanoresponses that cells have to external forces, i.e., mechanotransduction. Information gained from these studies has been utilized in computational models that address cell mechanics as a collection of biomechanical and biochemical processes. These models have been advantageous in explaining experimental observations by providing a framework of underlying cellular mechanisms. They have also enabled predictive, in silico studies, which would otherwise be difficult or impossible to perform with current experimental approaches. In this review, we discuss these novel, experimental approaches and accompanying computational models. We also outline future directions to advance the field of cell mechanics. In particular, we devote our attention to the use of microposts for experiments with cells and a bio-chemical-mechanical model for capturing their unique mechanobiological properties.