I'll discuss joint work with Brent Doran and Dave Jensen in which we use an "algebraic uniformization" of \bar{M}_{0,n} to study the Cox ring and effective cone.  This construction exhibits this moduli space as a non-reductive GIT quotient of affine space and reveals a precise sense in which it is "one G_a away" from being a toric variety.  We find, in particular, that for n \ge 7 the Cox ring contains far more information than the effective cone and that several new phenomena arise that do not occur for n \le 6.