We present a density functional formalism for the phase behaviour of side-chain liquid-crystalline polymers. The theory explicitly takes into account the full molecular geometry, the different character of the constituents, and the flexibility of the molecular components. We obtain results on bulk properties as well as the local distribution of orientational order within the polymers. The theory rules out the possibility of nematic-nematic phase transitions, and we observe a continuous crossover from oblate to prolate backbone conformations, in contrast to earlier predictions.