Multiscale modeling and simulation has received widespread applications in various scientific and engineering disciplines. Although these applications deal with a diverse range of systems and serve different purposes, they face a number of common challenges with respect to the construction, solution, and computer implementation of multiscale models. The solutions to these challenges could bring common concepts, methods, and tools that can be shared by different disciplines and facilitate new applications of this promising modeling paradigm. This paper attempts to outline the key aspects of these common challenges, identify the important issues of each aspect, and summarize progress to-date. Directions for future work are also suggested toward the formulation of the common conceptual and computational frameworks for multiscale modeling.