The moduli space \overline{M}_{0,n} of genus zero stable curves with n marked points is a compactification of the space M_{0,n} describing isomorphism classes of n distinct points in P^1. This beautiful space has been intensely studied by topologists and algebraic geometers. I will give a biased introduction to this moduli space, and some of the related mathematics, including combinatorial aspects, phylogenetic trees, the Gelfand-MacPherson correspondence, and will lead up to describing many sets of explicit equations for \overline{M}_{0,n}, which is joint work with Angela Gibney.