The paper is concerned with methods for computing the best low multilinear 
rank approximation of large and sparse tensors. Krylov-type methods have 
been used for this problem; here block versions are introduced. For the 
computation of partial eigenvalue and singular value decompositions of 
matrices the Krylov-Schur (restarted Arnoldi) method is used. We describe 
a generalization of this method to tensors, for computing the best low 
multilinear rank approximation of large and sparse tensors. In analogy to
 the matrix case, the large tensor is only accessed in multiplications 
 between the tensor and blocks of vectors, thus avoiding excessive memory 
 usage. It is proved that, if the starting approximation is good enough, 
 then the tensor Krylov-Schur method is convergent. Numerical examples 
 are given for synthetic tensors and sparse tensors from applications, 
 which demonstrate that for most large problems the Krylov-Schur method 
 converges faster and more robustly than higher order orthogonal iteration.