  We review recent progress towards the solution of exactly solved isotropic
vertex models with arbitrary toroidal boundary conditions. Quantum space
transformations make it possible the diagonalization of the corresponding
transfer matrices by means of the quantum inverse scattering method. Explicit
expressions for the eigenvalues and Bethe ansatz equations of the twisted
isotropic spin chains based on the $B_n$, $D_n$ and $C_n$ Lie algebras are
presented. The applicability of this approach to the eight vertex model with
non-diagonal twists is also discussed.
