3D chirality of anisotropic structures is associated with directionally asymmetric transmission (reflection and absorption) of linearly polarized electromagnetic waves. Different levels of total transmission (reflection and absorption) for the same linearly polarized wave incident on their front and back arise from different, e.g. x-to-y, linear polarization conversion efficiencies for opposite propagation directions of the incident wave and therefore the effect is referred to as linear conversion dichroism. The x-to-y and y-to-x polarization conversion efficiencies are interchanged for opposite directions of wave propagation. Linear conversion dichroism has been observed in metamaterials with intrinsic and extrinsic 3d chirality. Active metamaterials, where the effect can be turned on and off have been realized by controlling 3d chirality with phase transitions.