The Virtual Element Method (VEM) is a recent technology for the numerical approximation of partial differential equations on computational grids constituted by polygonal or polyhedral elements of very general shape. The aim of this work is to develop effective linear solvers for general order VEM approximations of three-dimensional scalar elliptic equations in mixed form and Stokes equations. To this end, we consider block algebraic multigrid preconditioners and balancing domain decomposition by constraints (BDDC) preconditioners. The latter allow us to use conjugate gradient iterations, although the algebraic linear systems resulting from the discretization of the differential problems are indefinite.