Based on a level set model, a topology optimization method has been suggested recently. Ituses a level set to express the moving structural boundary which can flexibly handle complex topo-logical changes. By combining vector level set models with gradient projection technology, the levelset method for topological optimization is extended to a topological optimization problem withmulti-constraints, multi-materials and multi-load cases. Meanwhile, an appropriate nonlinear speedmapping is established in the tangential space of the active constraints for a fast convergence. Then themethod is applied to structure designs, mechanism and material designs by a number of benchmarkexamples. Finally, in order to further improve computational efficiency and overcome the difficultythat the level set method cannot generate new material interfaces during the optimization process, thetopological derivative analysis is incorporated into the level set method for topological optimization,and a topological derivative and l Based on a level set model, a topology optimization method has been suggested recently. Ituses a level set to express the moving structural boundary which can flexibly handle complex topo-logical changes. By combining vector level set models with gradient projection technology, the levelset method for topological optimization is extended to a topological optimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, an appropriate nonlinear speed mapping is established in the tangential space of the active constraints for a fast convergence. Then themethod is applied to structure designs, mechanism and material designs by a number of benchmarkexamples. Finally, in order to further improve computational efficiency and overcome the difficulty of the level set method can not generate new material interfaces during the optimization process, thetopological derivative analysis is incorporated into the level set method for topological optimization, and a topologica l derivative and l