The recently proposed artificial media with negative magnetic permeability and left-handed metamaterials are revisited at the light of the theory of artificial bi(iso/aniso)tropic media. In particular, the existence of bianisotropic effects in those materials is investigated, making use of an approximate model. Some unexplained properties of the electromagnetic-wave propagation through these media, revealed by closer inspection of previous numerical simulations and experimental work, are highlighted. It is shown that these peculiarities are properly explained if the bianisotropy is explicitly accounted for. The bianisotropy is related to the existence of magnetoelectric coupling in the artificial constituents (artificial atoms) of the medium. A simple modification of the artificial atom that precludes the bianisotropy is also proposed.