A major challenge in the modeling of biological systems is the accurate description of physical, chemical, and biological phenomena over a wide range of spatial and temporal scales. In practice, various hierarchical modeling techniques have been explored. However, the concurrent coupling which is more relevant and ubiquitous in biological systems has not yet been fully understood. In this talk, a mathematical framework of concurrent multi-scale and multi-physics modeling of biological systems is laid out. In particular, two specific aspects of this modeling strategy will be elaborated. Firstly, the validity of the newly developed immersed continuum method (ICM) will be examined via a meshless finite element solid model coupled with the surround fluid. This new modeling method enables a unified treatment of flexible structures or solids moving in aqueous environment and the direct coupling with mass and heat transfer equations. Secondly, a finite temperature bridging scale approach is presented to link macroscopic computational mechanics with localized refinements at micro-or nano-scale using molecular dynamics. Finally, future work spanning the quantum and continuum length scales will be proposed.