  This chapter appears in "Fractional Quantum Hall Effects: New Development,"
edited by B. I. Halperin and J. K. Jain (World Scientific, 2020). The chapter
begins with a primer on composite fermions, and then reviews three directions
that have recently been pursued. It reports on theoretical calculations making
detailed quantitative predictions for two sets of phenomena, namely spin
polarization transitions and the phase diagram of the crystal. This is followed
by the Kohn-Sham density functional theory of the fractional quantum Hall
effect. The chapter concludes with recent applications of the parton theory of
the fractional quantum Hall effect to certain delicate states.
