In this talk, we will give some isoperimetric bounds for lower order eigenvalues of the Wentzell-Laplace on bounded domains of a Euclidean space or a Hardamard manifold, of the Laplacian on closed hypersurfaces of a Euclidean space or a Hardamard manifold and of a biharmonic Steklov problem on bounded domains of a Euclidean space. This talk is based on a joint-work with Prof. F. Du, Prof. Q.-L. Wang and Prof. C.-Y. Xia.