While the last decades have seen considerable efforts to control molecular packing in organic crystals, the idea of controlling packing in organic glasses is relatively unexplored. Glasses have many advantageous properties that crystals lack, such as macroscopic homogeneity and compositional flexibility, but packing in organic glasses is generally considered to be isotropic and highly disordered. Here we review and compare four areas of recent research activity showing control over anisotropic packing in organic glasses: (1) anisotropic glasses of low molecular weight organic semiconductors prepared by physical vapor deposition, (2) the use of mesogens to produce anisotropic glasses by cooling equilibrium liquid crystal phases, (3) the preparation of highly anisotropic glassy solids by vapor-depositing low molecular weight mesogens, and (4) anisotropic films of polymeric semiconductors prepared by spin-coating or solution casting. We delineate the connections between these areas with the hope of cross-fertilizing progress in the development of anisotropic glassy materials.