The electromagnetic field problem for general, linear, homogeneous bianisotropic media is studied for field dependence on one spatial coordinate only. Explicit solutions for the dyadic Green functions are presented, first in general, then with special emphasis on transverse bianisotropy and biaxiality. The results are amenable to straightforward numerical implementation. They will mostly serve for a better understanding of the wealth of electromagnetic phenomena in complex materials and complement experimental studies in appropriate restricted configurations.