  We review Maxwell's equations and constitutive relations for 3D bianisotropic
media in a generalized form: we consider all four variables and allow for
nonzero polarization or magnetization, and also nonzero nonzero magnetic charge
or current. After a discussion of general boundary conditions, we introduce a
time-harmonic variational formulation of linear Maxwell's equations within 3D
bianisotropic media in terms of the electric and magnetic fields. We showcase a
finite element approximation of our variational formulation, using
curl-conforming N\'ed\'elec edge elements of the first kind. Numerical examples
illustrate the convergence of the method.
