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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 forω/T � 10 whereωis the bremsstrahlung gluon energy. (iii) Finally, I report on perturbative calculations of ˆq. 1. Equivalence of BDMPS-Zakharov and AMY The calculation of gluon bremsstrahlung from high-energy particles traversing a quark-gluon plasma is complicated by the Landau-Pomeranchuk Migdal (LPM) effect: at high energy, the formation length for bremsstrahlung (the distance over which gluon or photon emission is coherent) becomes longer than the mean free path between scatterings. As a result, bremsstrahlung from successive scatterings cannot be treated as independent. For QED, Migdal solved this proble

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