  We present a summary of some recent theoretical results for matter-wave
patterns in Fermi and Bose-Fermi degenerate gases, obtained in the framework of
the quasi-mean-field approximation. We perform a dimensional reduction from the
three-dimensional (3D) equations of motion to 2D and 1D effective equations. In
both cases, comparison of the low-dimensional reductions to the full model is
performed, showing very good agreement for ground-state solutions. Some complex
dynamical regimes are reported too for the corresponding 1D systems.
