  The leading jet transport coefficients $\hat{q}$ or $\hat{e}_{2}$ encode
transverse or longitudinal momentum broadening of a hard parton traversing a
hot medium. Understanding their temperature dependence is key to appreciating
the observed suppression of high-transverse momentum probes at RHIC or LHC
collision energies. We present a first continuum extrapolated result of
$\hat{q}$ computed on pure SU(3) lattices with non-trivial temperature
dependence different from the weak-coupling expectation.
  We discuss our formalism and its challenges and status in view of obtaining
$\hat{e}_{2}$ or of unquenching the calculation. We consider a hard quark
subject to a single scattering on the plasma. The transport coefficients are
factorized in terms of matrix elements given as integrals of non-local
gauge-covariant gluon field-strength field-strength correlators. After the
analytic continuation to the deep-Euclidean region, the hard scale permits to
recast these as a series of local, gauge-invariant operators. The renormalized
leading-twist term in this expansion is closely related to static quantities,
and is computed on pure SU(3) lattices ($N_{\tau}=4,~6,~8,$ and $10$) for a
wide range of temperatures, ranging from 200MeV < T < 1GeV. Our estimate for
the unquenched result in $2+1$-flavor QCD has very similar features.
