Abstract: Taking into account the connotation and engineering demand of smart grid, this paper summarizes and extracts several basic scientific issues of smart grid during its construction and development process, including prediction, energy storage, control, dispatching, planning, assessment, and their common engineering game theory. These basic scientific issues respectively belong to the mathematics, control science or their cross discipline. The solution of these issues not only is the precondition of the realization of smart grid, but also can promote the application perspective of mathematics and control science. Thus, it possesses a significant value in the theory and engineering research.