In this talk I will discuss a notion of s-fractional mass for 1-currents in high codimension. Such a notion generalizes the notion of s-fractional perimeter for sets in the plane to higher-codimension, one-dimensional singularities. In particular, I will talk about some properties of 1-currents with finite s-fractional mass. These results are in collaboration with M. Cicalese, T. Heilmann, F. Onoue, M. Ponsiglione.