A hierarchy of theoretical models ranging from microscopic levels of description to effective rate equations is presented in terms of characteristic physical processes of the active semiconductor medium and the light field occurring in space and time. The applicability of the various levels of approximations of the hierarchy to describe the dynamics of spatially extended edge-emitting and vertical-cavity surface-emitting semiconductor lasers is discussed with characteristic results of numerical simulations. The influence of delayed optical feedback on the spatio-temporal dynamics is described. In particular, we show how suitably tailored delayed coherent feedback can be employed for the control of spatio-temporal dynamics.

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