  This paper gives a condensed review of the history of solutions to the
Euler-Poisson equations modeling equilibrium states of rotating stars and
galaxies, leading to a recent result of Walter Strauss and the author. This
result constructs a connected set of rotating star solutions for larger and
larger rotation speed, so that the supports of the stars become unbounded if we
assume an equation of state $p = \rho^\gamma$, $4/3<\gamma<2$. On the other
hand, if $6/5<\gamma<4/3$, we show that either the supports of the stars become
unbounded, or the density somewhere within the stars becomes unbounded. This is
the first global continuation result for rotating stars that displays
singularity formation within the solution set.
