Recent advances in micro- and nano-technologies and high-end computing have enabled the development of new experimental and modeling approaches to study biomechanics at the micro- and nano-scales that were previously not possible. These new cutting-edge approaches are contributing toward our understanding in emerging areas such as mechanobiology and mechanochemistry. Another important potential contribution lies in translational medicine, since biomechanical studies at the cellular and molecular levels have direct relevance in areas such disease diagnosis, nano-medicine and drug delivery. Thus, the developed experimental and modeling approaches are critical in elucidating important mechanistic insights in both basic sciences and clinical treatment. While it is hard to cover all the recent advances in this mini-review, we focus on several important approaches. For experimental techniques, we review the assays involving shear flow, cellular imaging, microbead, microcontact printing, and micropillars at the micro-scale, and micropipette aspiration, optical tweezers, parallel flow chamber, and atomic force microscopy at the nano-scale. In modeling and simulations, we outline the theoretical modeling for actin dynamics in migrating cell and actin-based cell motility in cellular mechanics, as well as the receptor-ligand binding in cell adhesion and the application of free, steered, and flow molecular dynamics simulations in molecular biomechanics. Relevant scientific issues and applications are also discussed.