A review is given of the one-dimensional, intrachain and intracolumnar, charge mobilities, Sµ1D, determined for p-bond-conjugated polymeric and for p-p-stacked columnar discotic materials using the pulse-radiolysis time-resolved microwave conductivity technique. The largest values, on the order of 10 cm2/(V s), are found for single-crystal polydiacetylenes polymerized either thermally or with low doses of radiation. Much lower values of Sµ1D, covering the range from 0.009 to 0.125 cm2/(V s), are found for solution-synthesized conjugated polymers for which six different backbone structures have been investigated. This is attributed mainly to their complex morphology and the resulting static disorder in the backbone structure. The highest mobilities for this class of material, ca. 0.1 cm2/(V s), are found for liquid crystalline derivatives of polyfluorene and poly(phenylenevinylene). Larger mobilities are found for discotic materials, with maximum values close to 1 cm2/(V s) in both the crystalline solid and liquid crystalline phases. This is attributed to their self-organizing nature and hence higher degree of structural order, which compensates for the weaker electronic coupling between monomeric units in the discotics compared with the covalently bonded conjugated polymers.