  We study the single soft-gluon current at two loops with two energetic
partons in massless perturbative QCD, which describes, for example, the soft
limit of the two-loop amplitude for $gg\to Hg$. The results are presented as
Laurent expansions in $\epsilon$ in $D=4-2\epsilon$ spacetime dimension. We
calculate the expansion to order $\epsilon^2$ analytically, which is a
necessary ingredient for Higgs production at hadron colliders at
next-to-next-to-next-to-leading order in the soft-virtual approximation. We
also give two-loop results of the single soft-gluon current in ${\cal N}=4$
Super-Yang-Mills theory, and find that it has uniform transcendentality. By
iteration relation of splitting amplitudes, our calculations can determine the
three-loop single soft-gluon current to order $\epsilon^0$ in ${\cal N}=4$
Super-Yang-Mills theory in the limit of large $N_c$.
