This talk summarizes conversion of large scale linear and nonlinear SDPs, which satisfies the sparsity characterized by a chordal graph structure , into smaller scale SDPs. The sparsity is classified in two types, the domain-space sparsity (d-space sparsity) for the symmetric matrix variable in the objective and/or constraint functions of the SDP, which is required to be positive semidefinite, and the range-space sparsity (r-space sparsity) for a linear or nonlinear matrix-inequality constraint of the SDP. Some numerical results on the conversion methods indicate their potential for improving the efficiency of solving various problems.