The Teichmuller space T(R) is the space of homotopy hyperbolic structures for a surface R. Weil introduced a Kaehler metric for T; the Weil-Petersson (WP) metric has negative curvature, is incomplete and is convex. Recent progress on the WP geometry include s understanding: the CAT(0) geometry, harmonic maps to T, the quasi-isometric equivalence of T to the Thurston-Hatcher pants complex, the behavior of geodesics, the dimension of quasi flats, as well as the Alexandrov tangent cone for the (partial compactification) the augmented Teichmuller space T-bar . A summary of select results on the geometry for one dimensional Teichmuller spaces will be presented. Properties of the geometry will be used to give a geometric construction of a geodesic dense in the unit tangent bundle of the moduli space. The approach contrasts with the standard constructions by coding and Markov partitions that require an appropriate notion of ideal boundary. The construction is also valid for hyperbolic Riemann surfaces with cusps. For a quick overview of WP geometry see http://arxiv.org/abs/0705.1105