I will present a survey of some recent mathematical work on rotating stars that is joint with Yilun Wu.   The rotating star is modeled as a compressible fluid subject only to gravity. Under certain conditions there exists a large family of solutions on which the supports of the stars become unbounded. The stars have a fixed mass and they rotate around a fixed axis at a speed that varies along the family.  I will also mention a more elaborate model, joint with Yilun Wu and Juhi Jang, that permits the entropy to be variable.