  In the setting of complete metric spaces, we prove that integral currents can
be decomposed as a sum of indecomposable components. In the special case of
one-dimensional integral currents, we also show that the indecomposable ones
are exactly those associated with injective Lipschitz curves or injective
Lipschitz loops, therefore extending Federer's characterisation to metric
spaces. Moreover, some applications of our main results will be discussed.
