Data mining technology is not only composed by efficient and effective algorithms, executed as standalone kernels. Rather, it is constituted by complex applications articulated in the non-trivial interaction among hardware and software components, running on large scale distributed environments. This last feature turns out to be both the cause and the effect of the inherently distributed nature of data, on one side, and, on the other side, of the spatiotemporal complexity that characterizes many DM applications. For a growing number of application fields, Distributed Data Mining (DDM) is therefore a critical technology. In this research paper, after reviewing the open problems in DDM, we describe the DM jobs on Grid environments. We will introduce the design of Knowledge Grid System.