t has been over two decades since m. gromov initiated the study of pseudo-holomorphic curves in symplectic manifolds. in the past decade we have witnessed mathematical constructions of gromov-witten theory for algebraic varieties, as well as many major advances in understanding their properties. recent works in string theory have motivated us to extend our interests to gromov-witten theory for deligne-mumford stacks. such a theory has been constructed, but many of its properties remain to be understood. in this talk i will explain the main ingredients of gromov-witten theory of deligne-mumford stacks, and i will discuss some recent progress regarding main questions in gromov-witten theory of deligne-mumford stacks.