Twenty years since the discovery of the Fractional Quantum Hall Effect:   current state of the theory
  The current state of the theory of the Fractional Quantum Hall Effect is critically analyzed, especially the generally accepted concept of composite fermions. It is argued that there is no sound theoretical foundation for this concept. A simple one-dimensional model is proposed, which presumably has an energy spectrum similar to that of the FQHE system. 
M.I. Dyakonov