  I report on some theoretical progress concerning the calculation of gluon
bremsstrahlung for very high energy particles crossing a weakly-coupled
quark-gluon plasma. (i) I advertise that two of the several formalisms used to
study this problem, the BDMPS-Zakharov formalism and the AMY formalism (the
latter used only for infinite, uniform media), can be made equivalent when
appropriately formulated. (ii) A standard technique to simplify calculations is
to expand in inverse powers of logarithms $\ln(E/T)$. I give an example where
such expansions are found to work well for $\omega/T \gtrsim 10$ where $\omega$
is the bremsstrahlung gluon energy. (iii) Finally, I report on perturbative
calculations of $\hat q$.
