As the frontier of biomechanics research, cellular and molecular biomechanics is an interdisciplinary research field at the cutting edge of applied mechanics and life science and biology, which brings us many challenging problems to the current theories and techniques in biomechanics due to its importance and complexity. This paper will give a brief review on several of these challenging problems and make some comments on the papers included in this special issue, such as the mechanical properties and modeling methods of cell, the modeling of mechanochemical couplig and multiscale modeling methods in cell mechanics, so as to stimulate the common interest within not only the biomechanics but also the applied mechanics community.