  In this talk, we discuss the soft-gluon resummation for a pair of Higgs
bosons in the dominant gluon fusion channel to next-to-next-to-next-to-leading
logarithmic (N$^3$LL) accuracy. Through the study, we achieve sub-percent level
accuracy in the uncertainties from the residual renormalisation and
factorisation scales, for both inclusive and differential mass distribution in
the infinite top quark mass limit. We also combine these results with the full
top mass dependent next-to-leading order calculations.
