We review recent theoretical developments in the study of the structure of jets that are produced in ultra relativistic heavy ion collisions. The core of the review focusses on the dynamics of the parton cascade that is induced by the interactions of a fast parton crossing a quark-gluon plasma. We recall the basic mechanisms responsible for medium induced radiation, underline the rapid disappearance of coherence effects, and the ensuing probabilistic nature of the medium induced cascade. We discuss how large radiative corrections modify the classical picture of the gluon cascade, and how these can be absorbed in a renormalization of the jet quenching parameter $hat q $. Then, we analyze the (wave)-turbulent transport of energy along the medium induced cascade, and point out the main characteristics of the angular structure of such a cascade. Finally, color decoherence of the in-cone jet structure is discussed. Modest contact with phenomenology is presented towards the end of the review.
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