The statistical physics of lyotropic polymer liquid crystals is reviewed and extended, an analysis being given of the effect of the third virial coefficient, charge, semiflexibility, bidispersity, and polydispersity. The isotropic-nematic phase transition is discussed for long rods along the lines of the virial expansion, and the influence of bidispersity and polydispersity is considered. For polyelectrolytes the effects of twist and an increased effective diameter on liquid crystal formation are treated. This is extended to bidisperse and semiflexible polyelectrolytes. The configurational entropy of nematic semiflexible polymers is calculated by different methods and is shown to differ markedly from that of rigid rods. The effect of semiflexibility on the phase transition is analyzed for both mono- and bidisperse systems, the theory agreeing well with data on slender polymer chains like schizophyllan and polyG-benzyl L-glutamate).