These lectures consist in an introduction to the microscopic transport processes arising in a semiconductor material and their description by means of the kinetic (Boltzmann) equations. Then a review of the hierarchy of diffusion models that can be deduced from the Boltzmann equation through various scaling limits will be given. These include the so-called `Spherical Harmonics Expansion' (or SHE) model and the related `Energy-Transport' and `Drift-Diffusion' models. Depending on the schedule, recently developped topics like heterojunctions, superlattice modeling or quantum-diffusion or kinetic-diffusion coupling will possibly be outlined.

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