The phase behavior of three N-alkyl-substituted perylene diimide derivatives is examined by differential scanning calorimetry and polarized optical microscopy. The occurrence of multiple phase transitions indicates several crystalline and several liquid crystalline phases. X-ray diffraction measurements show that the liquid crystalline phases display high structural ordering in all three dimensions: smectic layers are formed, and within these smectic layers an additional ordering in columns is observed. Molecular modeling confirms this result and substantiates smectic ordering with interdigitating alkyl chains that determine the distance between the smectic layers. The ordering in columns is favored by - interactions between the cofacially oriented perylene molecules and by the elliptic shape of the molecule. Finally, intermolecular dipole-dipole interactions between the carbonyl groups of the imide moieties cause the perylene molecules to orient on average with a slight rotation between neighboring molecules within a columnar stack. Following the determination of the electronic transition dipole moment, this orientation, which still involves substantial - interactions, could be confirmed by UV/vis spectroscopy of perylene aggregates. To gauge the potential of these materials as organic semiconductors, the charge carrier mobility of one of the perylene derivatives has been measured by pulse-radiolysis time-resolved microwave conductivity. A value in excess of 0.1 cm2 V-1 s-1 is found in the liquid crystalline phase, and a value in excess of 0.2 cm2 V-1 s-1 is found for the crystalline phase. These values are comparable with the highest values previously found for other discotic materials.