We discuss some aspects of isoperimetric inequalities for k-dimensional We discuss some aspects of isoperimetric inequalities for k-dimensional integral currents in complete CAT(0)-spaces and in complete metric spaces X admitting cone type inequalities. We first show that such X admit isoperimetric inequalities of Euclidean type for k-dimensional cycles. This means that the volume needed to fill a cycle of volume r is bounded above by Cr^(k+1)/k for some constant C depending only on k and X. This extends a result of M. Gromov from the context of Riemannian manifolds to that of metric spaces. We furthermore show: If all asymptotic cones of X have 'dimension' strictly less than k+1 in the sense that images of Lipschitz maps from R^(k+1) have (k+1)-dimensional measure 0 then X admits an isoperimetric inequality of sub-Euclidean type for k-dimensional cycles. As a consequence we obtain that a proper cocompact Hadamard space admits isoperimetric inequalities of sub-Euclidean type above the dimension of its Euclidean rank. In particular, isoperimetric inequalities can be used to detect the Euclidean rank of proper cocompact Hadamard spaces. A conjecture of Gromov asserts that such a space should even admit linear isoperimetric inequalities above its Euclidean rank. Our results can also be used to obtain new estimates for certain filling invariants at infinity of Hadamard spaces studied by Brady-Farb, Leuzinger and Hindawi.