  This article addresses the regularity issue for stationary or minimizing
fractional harmonic maps into spheres of order $s\in(0,1)$ in arbitrary
dimensions. It is shown that such fractional harmonic maps are $C^\infty$ away
from a small closed singular set. The Hausdorff dimension of the singular set
is also estimated in terms of $s\in(0,1)$ and the stationarity/minimality
assumption.
